Development of a laminar co-flowburner experiment to study the

combustion of modern automotive(bio-) fuels at elevated pressures

R.M.G. van der Zanden

Report number WVT 2008.03

Supervisors:prof. dr. L.P.H. de Goeydr. ir. C.C.M. LuijtenMsc M.H. de Andrade Oliveira

Master track Sustainable Energy TechnologyEindhoven University of TechnologyDepartment of Mechanical EngineeringSection Combustion Technology

MSc. Thesis, Eindhoven, Januari 2008

Summary

The depletion of fossil fuels and the growing demand for energy, boosts the search for alter-native energy sources. The use of bio-fuels for energy purposes is one of the alternatives. Anadditional advantage is that the combustion of these fuels can be considered environmentalfriendly and sustainable, if the supply chain is well managed. In the future, the number ofdifferent kinds of (bio-)fuels will increase, since there is a variety of sources available. In orderto do research on the characteristics of the fuels, an experiment is designed which makes itpossible to investigate a laminar co-flow diffusion flame in a pressurized environment, usingoptical diagnostic measurement techniques.

As a start, the work of a group of scientists have been studied, which has great experiencein using laser diagnostic techniques for investigating a laminar diffusion flame using mainlymethane as fuel. In their work they developed a co-flow diffusion burner which is used intheir experiments to measure temperatures, soot characteristics and major and minor species.They compared the data of their experiments with computational models, which show goodagreement. The co-flow burner is therefore considered as a base for the development of theburner for the experiments with liquid (bio-)fuels.

To determine the amount of liquid fuel necessary to operate the burner, the flame heightmodel of Burke and Schumann is used. A certain flame height, usually somewhere between 1and 10 cm, is necessary to perform the optical measurements. With the model of Burke andSchumann, extended with some additional calculations, it is possible to determine the flameheight as function of the required mass flow of fuel. The model is compared with a modelwhich uses the same starting point, but uses a different solution method. A comparison isdone using a correction factor, which is used in both models. An important parameter inthe models is the temperature. The temperature has a great influence on the determinationof the diffusion coefficient and the development of the velocity throughout the region of theflame which controls diffusion.

If the mass flow of the fuel is determined, a evaporator can be selected, to vaporize the liquidfuels considered for the experiment. A number of criteria has been set up to evaluate threedifferent evaporation devices, for example the quality and controllability of the vapor stream.The selected devices are: the hot plate evaporator, the controlled evaporator mixer and thecapillary force vaporizer. All the three devices use heat as the main variable for evapora-tion, since other variables, such as pressure are not ideal, because the whole system willbe pressurized. After the evaluation, the controlled evaporator mixer is chosen as the finalconcept, due to the great quality and controllability of the vapor stream. The evaporatorhas one main drawback, it has a temperature limit and is not able to vaporize heavy fuels.A solution to this problem is introduced, which uses the vapor pressure of the fuel at the

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limited temperature of the evaporator.

If the fuel is evaporated, it can be burned in a co-flow burner, which is specially designedto fit in a pressure vessel. In this case a cubically shaped pressure vessel is selected tofunction as high pressure environment. The vessel has the benefit of offering at least fouroptical access ports and additional holes to apply other equipment. The co-flow burner hasa flexible internal design to experiment with flow straitening material necessary to increasethe flame stability, especially when flames are burned at high pressures. The burner is alsoexternally heated to avoid condensation of the fuel vapor in the fuel tube at the center of theburner.

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Nomenclature

i molar stoichiometric coefficient []j diffusion flux [kg/m2s]k thermal conductivity [W/mK]p pressure 0.1[MPa] = 1[bar]r radial distance [m]t time [s]v velocity of gas [m/s]z vertical distance above orifice of inner tube [m]

A surface [m2]C concentration of combustible gas [mole/m3]C1 initial concentration (partial pressure) of combustible gas [mole/m3]C2 initial concentration (partial pressure) of oxygen [mole/m3]C0 = C1 + C2/i [mole/m3]D diffusion coefficient [m2/s]L radius of the inner or fuel tube [m]M molar mass [kg/mole]Q heat flow [W ]R radius of the outer tube of the co-flow burner [m]T temperature [K]X mole fraction [-]Y mass fraction [-]

density [kg/m3] mass flow [kg/s]

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Contents

1 Introduction 11.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Overall research overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.3 Assignment profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.4 Report outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2 Literature review 52.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.2 Experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.3 Diagnostic work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.4 Results and recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

3 Modeling flame shape 113.1 Simple flame height model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113.2 Burke-Schumann flame shape model . . . . . . . . . . . . . . . . . . . . . . . 123.3 Diffusion coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183.4 Pressure dependence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183.5 Reviewing the Burke-Schumann solution . . . . . . . . . . . . . . . . . . . . . 193.6 Results from modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

4 Fuel evaporation 264.1 Considered fuels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264.2 Evaporation concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

4.2.1 Evaporation principles . . . . . . . . . . . . . . . . . . . . . . . . . . . 284.2.2 Hot plate evaporator . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284.2.3 Controlled evaporator mixer . . . . . . . . . . . . . . . . . . . . . . . . 304.2.4 Capillary force vaporizer . . . . . . . . . . . . . . . . . . . . . . . . . . 31

4.3 Evaluation of evaporation concepts . . . . . . . . . . . . . . . . . . . . . . . . 324.4 Final evaporation concept . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

5 High pressure burner 375.1 Pressure vessel design options . . . . . . . . . . . . . . . . . . . . . . . . . . . 375.2 Burner design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

5.2.1 Co-flow burner evolution . . . . . . . . . . . . . . . . . . . . . . . . . . 385.2.2 Component integration . . . . . . . . . . . . . . . . . . . . . . . . . . 395.2.3 Strength calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405.2.4 Measures for increasing flame stability . . . . . . . . . . . . . . . . . . 425.2.5 Heating the burner . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

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5.3 Safety issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

6 Conclusions and Recommendations 466.1 Conclusions and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 466.2 Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

A Bronkhorst product training day notes 53A.1 Principles of a mass flow controller . . . . . . . . . . . . . . . . . . . . . . . . 53

A.1.1 Liqui-flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53A.1.2 EL-flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

A.2 Construction of a mass flow controller . . . . . . . . . . . . . . . . . . . . . . 54A.3 Controlled evaporator mixer . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57A.4 Calibration and measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

B Matlab scripts 60B.1 Centerline height of the flame as function of the mass flow . . . . . . . . . . . 60B.2 Flame height and fuel mole fractions as function of the mass flows . . . . . . 61B.3 Concentration fuel gas as function of the radius . . . . . . . . . . . . . . . . . 64B.4 solvez.m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

C Drawings of the high pressure burner 67

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List of Figures

1.1 A future prospective on the share of fuels used in cars [1]. . . . . . . . . . . . 21.2 An overview of the transition of the simple atmospheric gas burners to the

engine in the real situation, with respect to the possibility the technologiesoffer for experimental investigation. . . . . . . . . . . . . . . . . . . . . . . . . 3

2.1 A schematic drawing of the burner [18] . . . . . . . . . . . . . . . . . . . . . . 72.2 Measured (left) and computed (right) temperature profiles of a highly diluted

methane flame [9]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.3 Computed (left), LII (middle) and probe (right) soot volume fraction isopleths

of a ethylene flame [8]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

3.1 A simple layout of the burner with a cylindrically shaped flame . . . . . . . . 113.2 A simple layout of the burner . . . . . . . . . . . . . . . . . . . . . . . . . . . 133.3 Height of a CH4 flame with respect to the volume flow of the fuel at atmo-

spheric conditions. The temperature of the flame (Tflame) is obtained fromthe experiment of Den Blanken [28], which is approximately 1000 K . . . . . 21

3.4 Flame shape of a CH4 flame determined by calculating the concentrationderived by the corrected Burke-Schumann solution, with f = 2 mg/s, Tflame= 1675 K . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

3.5 Flame height lines calculated with respect to the mole fraction hexadecane(C16H34) and the gas speed at atmospheric conditions (a) and at elevatedpressure (b) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3.6 Centerline height of the flame (almost vertical lines) and fuel mole fractionlines with respect to the mass flows of (C16H34) and carrier gas (nitrogen(N2)) at atmospheric conditions (Tfuel = 473 K, Tflame = 1200 K) . . . . . . 25

4.1 Two sectional views of the hot plate evaporator of Vranos [36,37]. . . . . . . 294.2 The hot plate evaporator design of Preben Stobakk [38]. . . . . . . . . . . . . 304.3 A schematic lay out of a Controlled Evaporator Mixer. . . . . . . . . . . . . . 314.4 A schematic lay out of a Capillary Force Vaporizer [40]. . . . . . . . . . . . . 324.5 Vapor pressure chart of a range of hydrocarbons [41]. . . . . . . . . . . . . . . 354.6 A schematic overview of the experiment using the controlled evaporator mixer.

Explanation of the components: 1: pressure controller to control the accumu-lator pressure, 2: pressurized fuel accumulator (2l. storage tank), 3: fuel filter,4: liquid mass flow meter, 5: controlled evaporator mixer, 6: nitrogen gas bot-tle, 7: nitrogen mass flow controller, 8: air reservoir, 9: air mass flow meter,10: pressure controller to control total system pressure. . . . . . . . . . . . . 36

5.1 Options for a design of a high pressure vessel, which is able to withstand 3 MPa. 38

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5.2 The development of the co-flow burner. . . . . . . . . . . . . . . . . . . . . . 395.3 The definite pressure burner design. Explanation of the numbers: 1: pressure

vessel, 2: co-flow burner, 3: quartz window, 4: window support ring, 5: innerchimney, 6: top chimney. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

5.4 Schematic drawing used by calculating material strength. . . . . . . . . . . . 425.5 Radius of the outer wall of the pressurized burner as function of its internal

vessel pressure. The inner radius of the outer tube of the co-flow burner is 25mm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

5.6 The attachment of the co-flow burner to the pressure vessel: 1: co-flow burner,2: fuel supply tube, 3: large flow straightener, 4: small flow straightener, 5:heat insulating ring, 6: burner support ring. . . . . . . . . . . . . . . . . . . . 43

5.7 Temperature decrease managed by the insulating ring (PTFE) as function ofthe thickness of the ring. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

A.1 The outside and inside of a mass flow controller. . . . . . . . . . . . . . . . . 54A.2 Measurement principle of a EL-flow mass flow controller. . . . . . . . . . . . . 55A.3 The elements of a control valve assembly, in configuration applicable to the

CEM-module. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56A.4 The lay-out of the CEM-module. . . . . . . . . . . . . . . . . . . . . . . . . . 58

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Chapter 1

Introduction

1.1 Background

Due to the predicted scarcity of fossil fuels, the increasing environmental burden of consumingthese fuels and the increasing worldwide demand for energy, the need for alternative energysources will increase. The protection of the environment plays an increasing role in the humansociety and the emission of green house gasses, like the CO2 emission from the combustionof fossil fuels, is regarded as the main concern. Furthermore, the search for alternativesfor the depleting fossil fuels is an ongoing process. Within this process, renewable energysources are considered as an important alternative. One of the renewable alternatives isusing energy from biomass. Energy from biomass can be called renewable if the supplychain of the biomass is well managed, which means the carbon cycle has to be closed. Theraw biomass, like wood, crops, seeds or animal waste can be converted into bio-fuels, whichare ready to use in combustion engines. For transportation purposes, bio-fuels like: purevegetable oils, bio-diesel, biomass-to-liquid, gas-to-liquid, Dimethyl ether or ethanol, can beseen as a partial replacement of the fossil fuels in the future, see figure 1.1. Clean andefficient combustion of fossil fuels is an important issue within the international combustionengine community, the same holds for the alternative fuels. Clean combustion implies lowemissions of NOx, soot, unburned hydrocarbons and carbon monoxide. To accomplish this,further technological development of combustion systems and the engineering of the fuel aretwo important research areas. Engineering the fuel, by better understanding the combustionprocess on a molecular scale, will, together with a well developed combustion system, leadto a clean fuel for better efficiency.

1.2 Overall research overview

The research to combustion systems is focused on both simplified burner concepts, e.g. lami-nar flame burners, and complex practical combustion systems, e.g. optical engines, see figure1.2. The simple burner concept makes it possible to study in detail the chemical phenom-ena of complex fuel combustion and to compare the experimental data to numerical data.However the methods are largely limited to low pressures and fuels with a simple chemi-cal structure, such as methane. In contrast to the simple concept, the complex combustionsystems research, using real automotive (bio-)fuels and high pressures, are more focused onacquiring empirical data and most studies limit themselves to a kind of black box approach.

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Figure 1.1: A future prospective on the share of fuels used in cars [1].

To close the gap between the most simplified and the more complex systems, an idea is pro-posed to evaluate real automotive (bio-) fuels in a simple burner concept in high pressureconditions. To accomplish this, a burner concept has to be chosen which is capable to burnliquid fuels in a high pressure environment and the flame has to be comparable to numericallycomputed flame data. To be able to burn liquid fuels, the fuel first has to evaporate. For thisreason, an evaporator has to be constructed which is able to evaporate all the componentsof the automotive (bio-)fuels simutaneously (i.e., preventing preferential evaporation of thelighter components). After the fuel has evaporated, the fuel has to be burned in a laminarco-flow burner which would be placed in a high pressure vessel with optical access to studythe flame.

In the experiments, the flame will be investigated by using optical diagnostics. Initially, theemphasis of the investigation will be on the measurement of soot particles. The formation ofsoot is chosen for several reasons. First, soot can directly be measured using laser-diagnostics.Second, the results of the soot measurements provide an experimental database for the valida-tion of numerical models of soot formation in both simple gaseous fuels or modern automotive(bio-)fuels. And last, the possibility to control the fuel input mixture composition will resultin different amount of soot emission from the flame. For example, previous measurementsshow bio-diesel has a lower soot emission than regular diesel. Besides the measurement ofsoot emission, other quantities, like temperatures and mass flow of fuel and air, have to bemeasured and the measurement equipment has to be implemented in the experiment.

1.3 Assignment profile

The assignment of this graduation project is to develop an experimental set up to evaporateliquid automotive fuels and burn them in a co-flow laminar diffusion burner under elevatedpressures. The specifications of the set up, which is required for the experiments, are:

the system is able to burn a range of liquid fuels with high boiling points, the system must withstand 3 MPa (30 bar),

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Figure 1.2: An overview of the transition of the simple atmospheric gas burners to the engine

in the real situation, with respect to the possibility the technologies offer for experimental

investigation.

the set up creates the opportunity to optically investigate the flame in a high pressureenvironment.

The assignment can be split in a list of tasks, namely:

first a literature study on existing laminar diffusion burner experiments has to be carriedout,

a relation between fuel mass flow and flame height has to be derived, to determine therequired mass flows,

an evaluation of fuel evaporation concepts and high-pressure cell options is required, design a fuel evaporation system, design and construct the burner together with the high-pressure cell.

Additionally, the whole set up can undergo an initial run, to test if the systems are workingproperly.

1.4 Report outline

In chapter 2, this report will start with a literature study on the preliminary work of thescientists Long and Smooke [418]. They, together with other scientists, conducted laser-

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diagnostic experiments using a laminar co-flow burner which is made commercial available,to collect data from external experiments. The rough dimensions are going to be used in theburner for the experiment treated in this report. These dimensions are used in the modelingof the flame height and shape as function of the mass flow, as described in chapter 3. Afterthe modeling, in chapter 4, the fuel evaporation concepts are treated and evaluated. Theevaporation concept which is chosen has to supply the fuel vapor to the burner, which burnsthe fuel with a co-flow burner in a pressurized environment. The design of this burner istreated in chapter 5. This report finishes with some conclusions and recommendations.

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Chapter 2

Literature review

2.1 Background

As already mentioned in the introduction, simple laminar burner concepts allow thoroughinvestigation of the flame characteristics, theoretically as well as practically. To facilitatethe investigations, scientists all over the world have developed research tools to study flamestructures. Chemical reacting systems can be investigated by computational algorithms andmultidimensional laser imaging techniques [4], which have been developed in the past and arestill in development. Modeling multidimensional flames requires a large number of multidi-mensional equations that have to be solved for the elementary chemical species. This is oneof the main reasons why there have not been many combined computational/experimentalstudies of hydrocarbon flames, while flame modeling might be important for various practicalapplications.

The last decades, multidimensional imaging techniques, using optical laser setups, have be-come increasingly accurate. These techniques, like for example Laser Induced Fluorescence(LIF) or Rayleigh spectroscopy, have primarily been used to provide qualitative informationof turbulent flames. Since temporally resolved measurements are not necessary for lami-nar flames, the focus of a measurement can be directed towards quantitative measurementsand increasing the accuracy even more. This creates the opportunity to integrate signalsand compare multiple measurements performed under different circumstances. Long andSmooke, together with other scientists and researchers [418], have studied axisymmetriclaminar diffusion flames burning several gaseous fuels using several laser imaging techniques.Together with the experiments, numerical models are derived and computed. Within thenumerical models the governing conservation equations of mass, momentum, species balanceand energy are solved. This solution is accomplished using detailed transport and finite ratechemistry sub-models, such as GRI Mech, which is essentially a list of elementary chemicalreactions and reaction rate constants applicable to methane gas flames [4,6,19]. These mod-els are used to predict velocities, species mass fractions and temperature fields up to twodimensions within a flame of interest.

Another important combustion phenomenon is the formation of soot, due the fact that soot

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creates air pollution and as a consequence increases health concerns. Soot particles areformed out of steadily growing polycyclic aromatic hydrocarbon structures. Soot formationis, therefore, also subject for experimental interest and numerical modeling. In modeling, sootparticles are represented by solid carbon spheres and the kinetics are modeled using transportconservation equations, which include coalescence, surface growth and oxidation [8, 15, 23].While temperatures, velocities and species mass fractions, measured in experiments andcomputed in models, are quantitatively fairly comparable, even in sooty diffusion flames,the comparison between calculated and measured soot profiles is still insufficient. Therefore,further investigations, both theoretically and experimentally, are necessary to be able topredict the level of soot formation of different types of fuels. Besides this challenge, themeasurements of other combustion properties, like species mass fractions are also still subjectfor improvement, especially in case of non-gaseous fuels, like the automotive (bio-)fuels relatedto the experiment treated in this report.

2.2 Experimental setup

To generate axisymmetric laminar diffusion flames, Long et al. [418] have developed a burnerwhich is based on the original burner concept treated in the article of Burke and Schumann [2].The concept of the burner implies two concentric circular tubes, which make it possible tocreate a co-flow of a fuel and an oxidizer stream, as can be seen in figure 2.1. While the fuelflow is forced through the inner tube, the oxidizer flows through the space between the innerand the outer tube. In the first experiments a comparable burner design of Mitchell [3] isused, which consists of a 12.7 mm diameter internal fuel tube and a 50.8 mm diameter outeroxidizer tube. This burner was used in an experiment to validate a numerical model whichwas able to determine velocities, temperatures and major species concentrations. The mea-surements were performed using a quartz measurement probe and online mass spectrometryto measure species mole fractions and uncoated thermocouples to measure temperatures. Tocreate uniform exit flows, the burner was provided with a perforated solid brass disk, whichserved as the burner plate. During the experiment the flame was stabilized using a pyrexglass cylinder which served as a shield and also defined the boundaries of the system. Mea-surement resolution was created using an x-y and an x-z positioner.

The same burner configuration was used in preliminary work of Long et al. [418], al-though they used different fuel and oxidizer tube diameters. In some of their investiga-tions, [8, 10, 1518], the measurements were performed using both the probing technique aswell as laser imaging techniques. This was done to evaluate the different techniques andto compare the experimental data with the theoretical models. Since the last decade, thedimensions of the burner of Long and Smooke became standardized. The fuel tube was setto 4 mm inner diameter and the outer oxidizer tube was set to 50 mm inner diameter. Thiswas done to collect measurement data from different experiments using the same burner. Forthat purpose, the burner was made commercially available for other parties, which createsthe opportunity to expand the collection of measurement data.

Characteristic measured quantities of flames are generally temperature, species concentrationand soot volume fraction. These quantities are also of interest in the experiments performedby Long et al. [418] and are measured using probing and laser techniques. The laser tech-niques comprehend mainly Rayleigh or Raman spectroscopy, Laser Induced Fluorescence

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Figure 2.1: A schematic drawing of the burner [18]

(LIF) and Laser Induced Incandescence (LII). Typical equipment used in an experiment car-ried out in the laser laboratorium includes a second or third harmonic Nd-YAG laser, whichpumps a dye laser in case of LIF, line or sheet forming optics, optical filters and an intensifiedcharge coupled device (ICCD), in case of LIF combined with a spectrograph. The equipmentis mostly aligned to perform two dimensional measurements, which implies a laser sheet hasto be formed, while the signal is detected perpendicular to the formed sheet. This setup ap-plies, more or less, the same for all the different laser imaging techniques mentioned. Typicalequipment used in the probing measurements are thermocouples, especially for measuringtemperatures and thin quartz tubes, combined with an online mass spectrometer, used forthermophoretic sampling. The fuels used in the experiments are mainly methane and ethy-lene and are in all cases diluted with nitrogen gas to create fuel mass fractions from 0.3 to 1.Typically a fuel mass fraction of around 0.5 is used in the majority of the investigations. Airis commonly chosen as the oxidizer. Both the oxidizer and the fuel gas mixture streams arekept at an equal uniform velocity, which is 35 cm/s in all the experiments except for [16,17].

2.3 Diagnostic work

In the last decade, different types of experiments have been executed using the burner. Con-tinuing research interest is the formation of NOx due to combustion. Especially short-livedspecies like CH and OH are subject for investigation. Therefore, experiments using laser imag-ing techniques are extremely important to validate numerical models. Long et al. [46, 12]used LIF to measure NO and chemically exited OH and CH radicals, by illuminating theflame with a second or third harmonic Nd-YAG pumped dye laser. The measured LIF signalshave to be converted into quantitative concentration measurements made possible throughcalibrations and corrections. The somewhat problematic calibration of the LIF signal is doneby Raleigh scattering, using the same optical setup [6,12]. Rayleigh scattering is furthermoreextensively used for temperature measurements, where number densities are measured andconvert into temperatures using the ideal gas law, whereas Stokes-shifted vibrational Raman

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spectroscopy is focussed on measuring major species, for example N2, O2, CO2, CO, H2O andfuel concentrations, for example treated in [7,9,10,12,13]. To bridge the gap between laminarand turbulent combustion, the experiments in [7, 13] treat the study of forced time-varyinglaminar flames for temperature and species concentrations using the burner combined witha sound speaker and Rayleigh and Raman spectroscopy. An additional laser technique, Par-ticle Image Velocimetry (PIV), is used in these experiments to measure the cyclic fuel tubeexit velocities by seeding the fuel with particles. Another, relatively unconventional, laserdiagnostic method is taking the difference between the polarized and depolarized componentsof the Rayleigh signal, or a suitable linear combination, to measure fuel concentrations, asdescribed in [11]. While the depolarized signal, caused by non isotropic (i.e. spherically sym-metric) scattering objects, is 100 times smaller than the polarized signal, it is still 10 timeslarger than the Raman scattering. This method leads to the increase of the post-processedsignal-to-noise ratio of the effective fuel concentration image, if the depolarization ratio ofthe fuel component is sufficiently different from that of the oxidizer. This results in higheraccuracy fuel concentrations if the measurements are performed with diluted fuel, comparedto measurements with Raman spectroscopy [11]. This technique holds also for higher densityfuels, which creates opportunities when diluted and evaporated liquid fuels are considered.

Like stated before, the formation of soot is also an interesting combustion phenomenon andthere are various techniques to measure it. In the articles of Long et al. [810,14,15,18] severaltechniques to measure soot distributions are treated. They can simply be divided in probingand laser techniques, which are both compared with computational models. In the probingtechniques, described in [8,10,14,15] an uncoated thermocouple is used for spatially measuringtemperatures. An additional use of the thermocouple, apart from measuring temperatures, ismeasuring soot volume fractions. To be able to measure soot volume fractions, a technique isdeveloped which uses the error in the temperature measurement due to soot deposition, whenthe thermocouple junction is held into the flame [20]. This technique is called thermocoupleparticle densitometry (TPD) and has an absolute uncertainty of 50%. This technique isfairly comparable to thermophoretic sampling, which uses a quartz microprobe and analysesthe samples with an online mass spectrometer and has an absolute uncertainty of 30%. Ifa stable and stationary flame is formed, the probing techniques are capable to measure thesoot volume fractions in two dimensions, resulting in 2-D images. These images are comparedwith more sophisticated laser imaging techniques. The laser technique treated in [8,9,14,18]is Laser-induced incandescence (LII). Preliminarily to the LII measurements, Rayleigh andRaman spectroscopy measurements are performed, to measure, respectively, the temperature,and fuel and oxygen concentrations of the laminar diffusion flame. The LII signal is calibratedusing the probe measurements as in [8] or using an online extinction method, as in [18], whichis an alternative laser technique using the same optical setup as the LII measurement, but iscarried out with a lower laser fluence to avoid unwanted LII effects. Furthermore, all imagesare corrected for optical throughput, background scattering signals and non-uniformities inthe beam profile.

2.4 Results and recommendations

In all the articles treated in this section [418], the numerical models in the work of Longand Smooke are compared with experimental data, both qualitatively and quantitatively.Concerning major and minor species and temperature, the computational models predicted

8

the outcome to within experimental error, over most of the parameter range [6,810,12]. Oneof the main problems with respect to these measurements was the fluorescence interferencesfrom species on the fuel rich, or oxygen free, side of the flame front, as experienced in [9].This problem, however, was investigated in [10], which has resulted in significantly improvedsignal-to-noise ratio of the Rayleigh (temperature) and Raman (species mole fractions) mea-surements. This was achieved by using a programmable polarizer and taking the differenceof the detected light intensities under two orthogonal linear polarizations that were paralleland perpendicular to the linearly polarized laser source [10]. Furthermore, the effects of fueldilution with nitrogen has been investigated in [9]. This resulted in a blow-off limit reachedat a fuel mixture of 40% methane and 60% nitrogen. In this condition the flame is highlylifted, but the computational predictions have a strong deviation compared with the temper-ature profile measured by Rayleigh scattering, as can be seen in figure 2.2, and needs furtherinvestigation [9].

Figure 2.2: Measured (left) and computed (right) temperature profiles of a highly diluted

methane flame [9].

Regarding soot volume fraction measurements, the computational models underestimate peakvalues by 20% compared to experimental data [8], which can be considered as fairly good. Onthe other hand, the model has some difficulty in accurately reproducing the distribution ofsoot formed from the centreline to the wing of the flame, as can be seen in figure 2.3. In thisregion, the peak soot volume fractions are underestimated by a factor of about three [15].This underestimation is related to too low predicted temperatures, due to heat radiationfrom the base of the flame to the burner exit, which causes low computed values of criticalsoot growth species, such as acetylene and benzene. In the study of [8], the formation ofbenzene as a limit to the soot interception process was confirmed. If the simulation of heatradiation in the computational model is discarded, the predicted peak soot volume fractionsincrease by a factor of three [15]. This heat problem is further investigated in [18], where theyincreased the peak centreline to wing temperatures and produced better results in terms ofhigher peak volume fractions. It was also shown that the soot particle sizes vary significantlywith the location in the flame [15]. The particle diameter grows much more slowly along the

9

centreline of the flame than in the wings.

Figure 2.3: Computed (left), LII (middle) and probe (right) soot volume fraction isopleths

of a ethylene flame [8].

10

Chapter 3

Modeling flame shape

3.1 Simple flame height model

Figure 3.1: A simple layout of the burner with a cylindrically shaped flame

In optical diagnostics, studying flames, the surface of the flame perpendicular to the flameaxis is a relevant issue, especially if spatially resolved measurements are considered. In caseof diffusion flames, the shape roughly depends on the fuel supply tube diameter and the massflow of the fuel. With a fixed burner geometry, the height of the flame can be adjusted byadjusting the fuel mass flow. Typical flame heights in experiments are in the range of 10to 100 mm [418]. In order to determine the flame height as function of the fuel gas flowof several hydrocarbon fuels a relation between these parameters has to be derived. For aninitial approach Ficks first law of diffusion is used. In this approach, the flame is assumedto have a cylindrical shape, of which the height is equal to the height of the flame at thecenterline of the burner. According to Ficks law, the mass flux of a diffusing species can bewritten in cylindrical coordinates as follows:

11

j = DdYdr

. (3.1)

The parameterD represents the coefficient of diffusion, the density and Y the mass fraction.In this case the diffusion flux has the unit kg/m2s. A first approximation is that in the centerof the cylinder (r = 0): the fuel mass fraction, Yf , equals 1 and at the edge of the cylinder(r = L), Yf equals 0. In that case it can be stated that dY = 1 over a distance L, this impliesthat equation (3.1) becomes:

j DL. (3.2)

Using the principle of conservation of mass, the mass flow of fuel (m) can be written as:

m = 2piLhj = 2pihD = piL2vu, (3.3)

where h represents the height of the cylindrically shaped flame, L the radius of the fuel supplytube and vu the fuel gas velocity. This results in an expression of the flame height:

h L2vu2D

. (3.4)

The same solution is found if nitrogen is introduced as an inert gas to dilute the fuel stream(YN2 = 1 Yf , with Yf < 1):

piL2vuYf 2pihDYf h L2vu2D

. (3.5)

This simple solution, derived from Ficks first law of diffusion, assumes a cylindrical shape.Discarding this suggested shape presumably will lead to a more accurate solution. This isdone using a model proposed by Burke and Schumann, which will be treated in the nextsection.

3.2 Burke-Schumann flame shape model

Burke and Schumann [2] defined diffusion flames as flames in which the fuel gas and the airmeet coincident, with the occurrence of combustion. A typical burner of diffusion flames iscalled a laminar co-flow burner and exists of two vertical concentric tubes, of which the centertube is used to supply the fuel gas, while the outer tube functions as oxidizer supply. If theflame is ignited at the end of center tube and the velocity of both gases are the same andkept constant, it will produce a steady flame of definite shape. In order to mathematicallydefine the shape, so the height of the flame as function of its radius, certain fundamentalassumptions must be made. These assumptions are:

1. the mass-averaged velocity of the gas and air parallel to the flame axis is constant, i.e.v = constant,

2. the coefficient of diffusion is constant throughout the regions of the flame which controldiffusion, i.e. D = constant,

3. the diffusion is wholly radial, i.e. axial diffusion may be neglected,

4. admixture of the two gas streams occurs by diffusion only.

12

Figure 3.2: A simple layout of the burner

Assumptions 1 and 2 are debatable, but for simplification they are considered to be legiti-mate, while the third assumption will be valid only for fairly tall flames, but the mathematicaltreatment of short flames remains essentially the same. If tall flames are considered, the thick-ness of the flame front, in most cases, is so small that it may be treated as a geometricalsurface. This surface is created by the diffusion of the fuel gas outwards and the oxygeninwards regarding stoichiometric combustion. The oxygen combines with the gas to form aneutral product. The equations of diffusion of these gases are a part of the mathematicalanalysis. To determine the flame front, the oxygen is regarded as a negative fuel gas. Thisimplies, positive gas, referring to the fuel gas, diffuses into negative gas and the flame frontwill be determined by the surface where the concentration of the fuel gas is zero. Thus, themathematical problem is reduced to the diffusion of one single gas having a certain initialdistribution and subjected to certain boundary conditions.

As a start, the non-steady species continuity equation is rewritten. A general form of thisconservation equation for species A is:

AYAt

+ ~ (~vYA) = ~ (D~YA) A (3.6)

where A represents the rate of consumption of mass of species A. Regarding axi-symmetricconditions, this equation can be written in cylindrical coordinates, neglecting axial diffusionas stated in assumption 3:

13

YAt

=D

r

r

(rYAr

)[1r

(rvrYA)r

+(vzYA)

z

] A (3.7)

Using the overall continuity equation:

1r

(rvr)r

+(vz)z

= 0 (3.8)

and considering a steady state condition, equation (3.7) can be written as:

vzYAz

=D

r

r

(rYAr

) vr YA

r A (3.9)

The velocities of the gasses in radial direction are assumed to be very small (vr vz). Asa result the term containing vr can be neglected. In their work, Burke and Schumann intro-duced the variable C, which represents the concentration of fuel gas at any point, consideringthe oxidizer as a negative fuel gas. This concentration can be written as: CA = YA/MA,with species A representing the fuel gas. Since there is no consumption of gas, or species A,A can be neglected. This information, together with equation (3.9) leads to the followingequation of diffusion, also described in the work of Burke Schumann [2]:

C

z=

D

vz

(2C

r2+1r

C

r

). (3.10)

The solution of equation (3.10) can be derived using the method of separation of variables:

C(r, z) = R(r)Z(z) (3.11)

and making the following substitutions:

C

z= R(r)Z (z), (3.12)

2C

r2= R(r)Z(z) and (3.13)

C

r= R(r)Z(z). (3.14)

Inserting the equations (3.12), (3.13) and (3.14) into, (3.10) leads to:

RZ =D

vz

(RZ +

1rRZ

). (3.15)

Rewriting this equation and introducing the symbol , results in:

Z

Z=

D

vz

(R + 1rR

R

)= . (3.16)

By splitting equation (3.16), two solvable differential equations are created:

Z = Z and (3.17)

R +1rR = vz

DR. (3.18)

14

The general solution of equation (3.17) and (3.18) can be derived as, respectively:

Z = E1 exp(z) and (3.19)

R = E2J0

(vzD

r

)+ E3Y0

(vzD

r

). (3.20)

E1, E2 and E3 are constants. The expressions J0 and Y0 are the Bessel functions of the firstand the second kind respectively. For Y0 counts: if r0 the solution becomes: R(r) and is inconsistent. Consequently, Y0 is discarded. Using equation (3.11), the solution forthe gas concentration becomes:

C(r, z) = R(r)Z(z) = EJ0(r) exp(D

2z

vz

), with: =

vzD

. (3.21)

The boundary conditions are:

C

r= 0, when: r = 0 and r = R. (3.22)

When one of the boundary conditions is merged into the solution, the following expressioncan be used to determine :

J1(R) = 0. (3.23)

This expression has an infinite number of positive roots such that:

R = n, with: n = 1, 2, 3, . . . (3.24)

Therefore, for each root n, a corresponding value of n can be obtained, so:

n =nR. (3.25)

The new solution becomes a linear combination of all possible solutions:

C(r, z) =n=1

EnJ0(nr) exp(D

2nz

vz

). (3.26)

Since the burner consists of a fuel gas and the oxygen is regarded as negative fuel gas, aconcentration C2 of oxygen will be equivalent to C2/i fuel gas, where i represents themolar stoichiometric coefficient. The following initial conditions can be used to determinethe constant En:

C(r, 0) ={

C1 from r = 0 to r = L;C2i from r = L to r = R.

(3.27)

The initial condition over the whole domain [0, R] is multiplied by rJ0(mr):

n=1

EnrJ0(nr)J0(mr) = rJ0(mr)C(r, 0) (3.28)

and integrated over this domain:

15

n=1

En

R0

rJ0(nr)J0(mr)dr = R0

rJ0(mr)C(r, 0)dr (3.29)

The last equation is written as:

n=1

EnImn = R0

rJ0(mr)C(r, 0)dr (3.30)

Equation (3.23) shows that the expression nR gives the zero solutions of the Bessel functionJ1, but this orthogonality is not applicable to the Bessel function J0. This requires to rewritethe Bessel function J0 to J1 to use the orthogonal property of J1 and solve equation (3.29):

Imn = R0

rJ0(nr)J0(mr)dr =12n

nR0

(nr)J0(nr)J0(mr)d(nr) (3.31)

Using the substitutions x = nr, n = nR and the property of the Bessel function xJ0(x) =[xJ1(x)] to simplify the derivation:

12n

n0

xJ0(x)J0

(mn

x

)d(x) =

12n

n0

[xJ1(x)]J0(mn

x

)d(x) (3.32)

Partial integration can be used to solve equation (3.32):

12n

n0

J0

(mn

x

)d(xJ1(x)) =

12n

[xJ0

(mn

x

)J1(x)

]n0

12n

n0

xJ1(x)d(J0(mn

x))

(3.33)Using the property of the Bessel function [J0(x)] = J1(x), a first solution of the integrationcan be derived:

Imn =12n

[(n)J0

(mn

n

)J1(n)

]+

12n

n0

xJ1(x)J1

(mn

x

)mn

dx (3.34)

Using another property of the Bessel functionJ1(x)dx = J0(x) and the substitutions:

x = nr, n = nR and J1(n) = 0, this solution becomes:

Imn =mn

R0

rJ1(nr)J1(mr)dr =mn

mn12R2 (J0(nR))

2 (3.35)

Where mn represents the Kronecker delta, which is defined as:

mn ={

1 if m = n;0 if m 6= n.

Equation (3.30) can now be written as:

En12R2J20 (nR) =

R0

rJ0(nr)C(r, 0)dr = n (3.36)

To be able to extract the constant En, the integral of the last expression have to be solved.This is done by using the initial conditions of equation (3.27):

16

n = R0

rJ0(nr)C(r, 0)dr = C1 L0

rJ0(nr)dr C2i

RL

rJ0(nr)dr (3.37)

To simplify the derivation, again the substitution x = nr is made:

n =C12n

nL0

xJ0(x)dx C22ni

nRnL

xJ0(x)dx (3.38)

The solution of the integral is:

C12n

[xJ1(x)|nL0 C22ni

[xJ1(x)|nRnL =C12n

[nLJ1(nL)] C22ni

[nLJ1(nL)] (3.39)

keeping in mind J1(nR) = 0. Rewriting the expression results in:

n =1n

(C1 +

C2i

)LJ1(nL) C0L

nJ1(nL) (3.40)

introducing the term C0 = C1 + C2i . If this solution is now inserted into equation (3.36), theconstant En can be derived:

En12R2J20 (nR) =

LC0n

J1(nL) (3.41)

which gives:

En =2LC0R2

J1(nL)n (J0(nR))

2 (3.42)

Next, the solution of equation (3.26) can be rewritten as:

C(r, z) =2LC0R2

n=1

1n

J1(nL)J0(nr)(J0(nR))

2 exp(D

2nz

vz

)(3.43)

Since the the concentration C is considered as the fuel gas, which is consumed till C becomes0, and conservation of mass is respected, the solution should be corrected for the concentrationat a far distance above the burner exit. This is done by looking at the situation when thefuel and oxidizer are initially mixed over the whole of the burner width. This concentration,(C), is a homogeneous mixture of the fuel and oxidizer concentrations, so that:

piR2C = piL2C1 pi(R2 L2)C2i. (3.44)

If this expression is rewritten, using C0 = C1 + C2/i and added to the solution of equation(3.43), the final solution becomes:

C(r, z) = C0L2

R2 C2

i+2LC0R2

n=1

1n

J1(nL)J0(nr)(J0(nR))2

exp(D

2nz

vz

). (3.45)

This expression is used in the calculations of the flame height (z) as function of the gas velocity(vz), and fuel and oxidizer concentrations (C1 and C2). The next step is the calculation ofthe diffusion coefficient, this is treated in the next section.

17

3.3 Diffusion coefficient

In the first section of this chapter, Ficks law is used to derive the flame height. This law isbased on mass transport caused by concentration gradients and states that the mass flux j isproportional to the concentration gradient. The coefficient of proportionality is the diffusioncoefficient D. The diffusion coefficient can be estimated using an intermolecular model ofrigid spheres, representing the molecules of the fluid. If two fluids are considered, the binarydiffusion coefficient DAB can be calculated for a mixing process of a compound A into acompound B using the equation of Chapman and Enskog [21,22]:

DAB =0.00266T 3/2

pM1/2AB

2AB

, (3.46)

where p is the ambient pressure in [bar], T is the absolute temperature of the environment in[K], AB is the characteristic length in [A] andMAB represents the average molecular weight,or the reduced mass, of the fluids in [g/mole]. The latter can be derived from:

MAB = 2(

1MA

+1MB

)1, (3.47)

whereMA andMB are the molar mass of the fluids A and B, respectively. Since, in practice,the molecules are not perfect rigid spheres, the model has to be corrected for this imperfection.This correction is done via a factor called the reduced collision integral D, which correctsequation (3.46), which can now be written as:

DAB =0.00266T 3/2

pM1/2AB

2ABD

. (3.48)

To make it more convenient to calculate the binary diffusion coefficient without the knowledgeof molecular physics, like the characteristic length and the collision integral, equation (3.48)is adapted as described in Poling et. al. [21, 22]:

DAB =0.00143T 1.75

pM1/2AB

[()

1/3A + ()

1/3B

]2 . (3.49)Where ()A and ()B represent the molecular properties of fluids A and B respectively.The values of can be obtained by literature [21, 22], for example for nitrogen: ()N2 =18.5 or for air: ()Air = 19.7. In case of hydrocarbon or oxygenated hydrocarbon fuels aformula can be used to derive the fuel property ()f , depending on the number of C-, H-and O-atoms in the fuel:

()f = 15.9[nC ] + 2.31[nH ] + 6.11[nO]. (3.50)

3.4 Pressure dependence

The velocities and the concentration of the vaporized fuel/nitrogen mixture and oxidizer,together with the diffusion coefficient are dependent on pressure. As shown in the previoussection the diffusion coefficient is inversely proportional to the pressure, see equation 3.49.If a constant mass flow is considered and the law of conservation of mass and the ideal gas

18

law are used, the velocity of the gas mixture can be written as a function of the mass flowand pressure:

v =mR0T

pAM. (3.51)

Where m is the mass flow of fuel gas, R0 is the ideal gas constant (8.314 [J/K mole]), Mis the mean molar mass of the gas mixture and A is the surface of the fuel tube aperture.In this case, both the diffusion coefficient and the gas velocity are inversely proportional tothe pressure. In the solution of the Burke and Schumann model, the diffusion coefficientis divided by the velocity, which, as a consequence, cancels out the pressure dependence ofboth quantities in the calculation of the flame height, provided that m is constant. Thismeans, the concentrations are the only quantity left which is directly dependent on pressure.In the article of Burke and Schumann [2], they state that the initial concentrations are equalto the partial pressure of the fuel in the fuel/nitrogen mixture. However, if the pressure isincreased, the concentration is directly proportional to the pressure. If the partial pressureof the fuel (f) in an ideal gas mixture can be expressed as:

pf = pXf , (3.52)

the concentration vaporized fuel in the fuel/nitrogen mixture is:

C1 =pXfR0T

=MN2fp

(MN2f +MfN2)R0T, (3.53)

where the pressure is expressed in bar. As can be seen in (3.53), the concentration can bedetermined by adjusting the fuel and nitrogen mass flows (f , N2), at a fixed pressure.However, the mole fraction of the fuel (Xf ) has an upper limit which depends on the tem-perature, due to the ability of the vaporizer to vaporize the fuel. More on this in the sectionof fuel evaporation.

The same holds for the oxidizer stream. The oxygen concentration in the oxidizer flow (forexample air) is also dependent on the pressure and can be expressed as:

C2 =pXO2R0T

, (3.54)

where XO2 is the mole fraction or volume fraction of the oxygen in the oxidizer stream.

3.5 Reviewing the Burke-Schumann solution

Since there are several assumptions made to find the solution of Burke and Schumann, treatedin section 3.2, it is wise to review the validity of these assumptions, starting with the fourassumptions stated at the beginning. The mass-averaged velocities of the gases and theirdirection parallel to the flame axis are not constant. Due to the heat release from the flame,the density of the isobaric stream will decrease, which will increase the velocity accordingto v = constant [24]. Furthermore, the initial velocity profile is not uniform in practice,because the velocity must approach zero at the walls. However, if experimental precautionsare made to enhance the flow, by using flow straightening elements, this imperfection can beminimized. Similar to the velocity disturbances, the diffusion coefficient is also subject to thevarying and uncertain temperatures within the regions of the flame which control diffusion,particularly if the values of D for the fuel and oxidizer differ considerably [24]. Neglecting

19

the axial diffusion is also assumed and is acceptable when the flame height is several timeslarger than the fuel tube diameter. However, for analytically determining the flame height,these assumptions are justified by the analytical simplifications they produce.

Another assumption is made regarding the velocities of the gases in the radial direction. Theyare assumed to be very small with respect to the axial velocity (vr vz), which cancels outthe term in equation 3.9 containing vr. However, this approach is invalid, due to the largecontribution of mass transfer in the radial direction. Consequently, the term containing vr isnot equal to zero, so:

vrYAr

6= 0. (3.55)To correct this error, Roper [25] proposed a method using the continuity equation, like inequation 3.8, together with the ideal gas law, which states = pM/R0T , where the pressureis assumed constant and the temperature depends on the height. Combining those twoexpressions, result in the following expression:

vr = T (vz/T )z

, (3.56)

In his papers [25,26], Roper uses a different approach to the solution of the partial differentialequation of 3.10. This solution method is previously derived by Hottel and Hawthorne [27]and is regarding the flame height at the centerline of the flame. Applying the condition,of only regarding centerline flame height, to the partial differential equation, the solution,according to [25] and [27] becomes:

C(z) = 1 exp(1/4), (3.57)The factor is expressed differently in the paper of Roper, compared to the paper of Hotteland Hawthorne. The latter used the following expression:

=Dz

R2v1, (3.58)

With v1 represents the velocity of the fuel gas mixture. In the derivation, Roper [25] usedthe expression stated in equation 3.56 and derived the following expression for :

=DzT1

R2v1Tflame, (3.59)

where T1 is the initial temperature of the fuel gas mixture and Tflame the temperature inflame conditions. The difference between the equations 3.57 and 3.59 is reduced to the cor-recting factor Tflame/T1, which can be multiplied by the velocity of the gas mixture v1. Thiscorrection factor can also be applied to the solution of Burke and Schumann, by multiplyingvz by the factor Tflame/T1. A comparison between the solution of Roper and the slightlyadapted Burke and Schumann solution shows a good agreement. This comparison is treatedin the next section.

3.6 Results from modeling

All the calculations are performed in Matlab, the programming scripts can be found in ap-pendix B. The burner dimensions of the burner of Long and Smooke are used, so: L = 2mm

20

and R = 25mm. The solutions of the flame front position according to Burke and Schumannwhich holds when C(r, z) = 0 are derived using a build-in script of Matlab called fzero anduses a combination of bisection, secant, and inverse quadratic interpolation methods [29].In this section, the results of the modeling are treated. First, the centerline height of theflame is plotted against the volume flow of the fuel, as can be seen in figure 3.3. The Burke-Schumann solution is compared with the solution of Roper [25], the simple flame heightmodel using Ficks law described in section 3.1 and experimental data using the burner ofDen Blanken [28]. As stated in the previous section, the solution of Roper closely resemblesthe solution of Burke and Schumann if the temperature correction is applied. This in con-trast to the uncorrected initial solution of Burke and Schumann, which is far from similar tothe solution of Roper. Since the diffusion coefficient has a great influence on the behavior ofthe solution, it is kept equal in both the corrected and uncorrected Burke-Schumann solutions.

However, the diffusion coefficient of the solution of Roper is derived slightly different, since itis calculated using the temperature of the fuel gas and corrected by the following expression:

D = D0(Tflame/T1)1.67, (3.60)

where D0 is the diffusion coefficient calculated using the temperature of the fuel gas, T1 isconsidered to be the initial temperature of the fuel gas mixture and Tflame the temperaturein flame conditions [25]. This diffusion coefficient is 10% lower than used for the solution ofBurke and Schumann, which is calculated using the flame temperature.

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.40

0.02

0.04

0.06

0.08

0.1

0.12

Volume flow CH4 [ln/min]

Flam

e he

ight

[m]

Height of CH4 flame (Xf = 1, Tf = 300, Tflame = 1000, D = 2e4)

Ficks lawRoperBurke & SchumannBurke & Schumann corrected solutionExperimental data (R. den Blanken)

Figure 3.3: Height of a CH4 flame with respect to the volume flow of the fuel at atmosphericconditions. The temperature of the flame (Tflame) is obtained from the experiment of DenBlanken [28], which is approximately 1000 K

The advantage of the Burke-Schumann solution is the ability to calculate the concentrationof the fuel gas at any radius r and any height z. This creates the opportunity to determine

21

the outer shape of the flame, at the location where the fuel gas tends to go to zero. It isalso possible to visualize the effects of pressure using the information of section 3.4. Anexample of such an image of the flame shape can be found in 3.4(a), which is calculated foratmospheric pressure. At elevated pressures the flame tends to shrink in the radial direction,while keeping the same height, as can be seen in 3.4(b). For better visibility of the outershape and so the flame front, the concentration gradient in the figures is plotted using theinverse of the concentration and the surrounding air is set equal to zero. This increases thecontrast between fuel and oxidizer side of the diffusion flame.

Burner radius [m]

Flam

e he

ight

[m]

5 4 3 2 1 0 1 2 3 4 5x 103

0

1

2

3

4

5

6

7

8

9

10x 103

(a) Flame shape at atmospheric pressure (0.1 MPa)

Burner radius [m]

Flam

e he

ight

[m]

5 4 3 2 1 0 1 2 3 4 5x 103

0

1

2

3

4

5

6

7

8

9

10x 103

(b) Flame shape at 3.0 MPa pressure

Figure 3.4: Flame shape of a CH4 flame determined by calculating the concentration derivedby the corrected Burke-Schumann solution, with f = 2 mg/s, Tflame = 1675 K

In the previous modeling results, methane gas is used in the calculation. However, in theexperiments using vaporized automotive fuels which are mixed with a carrier gas, the molefraction of fuel (Xf ) is an important variable. Since the mole fraction determines the abil-ity of the liquid fuel to vaporize, a maximum mole fraction of fuel is fixed by its physicalproperties, more on this in topic in chapter 4. To determine the velocities of the fuel gasmixture at any fuel mole fraction and flame height required, figure 3.5 can be used. In thisfigure, the mole fractions are plotted against the gas mixture velocity, for a range of flameheights. While the upper limit of the fuel mole fraction is fixed by its properties, the velocityis preferably kept as low as possible, because the oxidizer stream velocity is equal to this ve-locity. The required mass flow of oxidizer is increasing extremely if the velocity is increased.Since lowering the mole fraction will result in a greater velocity, it is preferred to keep themole fraction close to the maximum mole fraction imposed by the fuel properties.

To specify the amount of fuel and carrier gas required to obtain a certain flame height, whichwill also be required by the specification of the fuel evaporator, figure 3.6 shows a contourplot of flame heights and fuel mole fractions as function of the fuel and carrier gas massflow (in this case hexadecane and nitrogen). In the contour plot, the almost vertical linesrepresent the flame height and the lines tending to go to zero are the mole fractions of fuel.Like in the previous result, the upper limit of the mole fraction of the fuel is fixed. If acertain flame height is required for an experiment, the mass flows of fuel and carrier gas can

22

be obtained by looking at the crossing between the lines of mole fraction and flame height.If the mass flows are determined, the specifications for the fuel evaporator are also determined.

23

0.01

0.01

0.01

0.010.01

0.02

0.02

0.02

0.02

0.03

0.03

0.03

0.03

0.04

0.04

0.04

0.05

0.05

0.05

0.06

0.06

0.06

0.07

0.07

0.08

0.08

0.09

0.09

Molefraction fuel (Xf)

Mix

ture

vel

ocity

(vm

ix) [

m/s]

Centerline height of the flame [m]

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1

0.1

0.2

0.3

0.4

0.5

0.6

(a) At atmospheric pressure (0.1 MPa)

0.01

0.01

0.02

0.02

0.02

0.03

0.03

0.03

0.04

0.04

0.04

0.04

0.05

0.05

0.05

0.06

0.06

0.06

0.07

0.07

0.08

0.080.09

Molefraction fuel (Xf)

Mix

ture

vel

ocity

(vm

ix) [

m/s]

Centerline height of the flame [m]

0.5 1 1.5 2 2.5 3x 103

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

0.22

0.24

(b) At 3.0 MPa pressure

Figure 3.5: Flame height lines calculated with respect to the mole fraction hexadecane(C16H34) and the gas speed at atmospheric conditions (a) and at elevated pressure (b)

24

0.01

0.01

0.02

0.02

0.02

0.03

0.03

0.03

0.04

0.04

0.04

0.05

0.05

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0.08

0.08

0.08

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0.09

0.09

0.1

0.1

0.1

0.1

0.15

0.15

0.15

0.2

0.2

0.2

Mas

s flo

w fu

el (

f) [kg

/s]

Mass flow nitrogen (

N2

) [kg/s]

Mol

e fra

ctio

n fu

el [

] and

cent

erlin

e heig

ht of

the f

lame [

m]

0.010.01

0.01

0.020.02

0.030.03

0.03

0.040.04

0.050.05

0.05

0.060.06

0.06

0.070.07

0.07

00.

10.

20.

30.

40.

50.

60.

70.

80.

91

x 10

6

0

0.2

0.4

0.6

0.81

1.2

1.4

1.6

1.82

x 10

6

Figure 3.6: Centerline height of the flame (almost vertical lines) and fuel mole fraction lineswith respect to the mass flows of (C16H34) and carrier gas (nitrogen (N2)) at atmosphericconditions (Tfuel = 473 K, Tflame = 1200 K)

25

Chapter 4

Fuel evaporation

4.1 Considered fuels

Like stated in the introduction, the diagnostic experiments will be mainly focussed on theinvestigation of modern automotive fuels and will also include bio-fuels. Besides regulargasoline and diesel, the fuels of interest are: (bio-)ethanol, bio-diesel, pure plant oil (PPO),dimethyl ether (DME) and liquified gas, biomass or coal (GtL, BtL, CtL). The mentionedfuels can be obtained from a range of sources and as a consequence the mixture of the chem-ical components can differ significantly. This has also an influence on the properties of thefuel, which means each fuel requires a standard for specifications and test methods. In caseof bio-diesel, or properly labeled fatty acid methyl ester, the standard is EN 14214 [30]. Thisstandard includes properties like density, viscosity and flash point. Using these standards,a tabel of general properties can be made, in comparison with fossil diesel, see table 4.1. Asimilar comparison can be made between bio-ethanol and fossil gasoline, see table 4.2.

Fuel Density Kinematicviscosity

Flashpoint

Caloric valueat 293 K

Cetanenumber

[kg/m3] [mm2/s] [K] [MJ/kg]Diesel 840 5 353 42.7 50Rapeseed oil 920 74 590 37.6 40Biodiesel 880 7.5 393 37.1 56Biomass-to-Liquid* 760 4 361 43.9 >70

Table 4.1: Parameters of bio-fuels in comparison with fossil diesel [30]. (*Values representFischer-Tropsch fuels)

Fuel Density Kinematicviscosity

Flashpoint

Caloric valueat 293 K

Octanenumber

[kg/m3] [mm2/s] [K] [MJ/kg] [-]Gasoline 760 0.6

Diesel, gasoline and their biological alternatives are fuels with a complex mixture of hun-dreds of hydrocarbons [31, 32]. The characteristics of these automotive fuels vary from eachother and even within one type of fuel, the chemical component mixture can vary from onesample to the other. Since these deviations are a disadvantage to the comparison of thefuels, especially in modeling, it is desirable to introduce surrogate substances which are ableto approximately reproduce thermo-physical and transport properties or create the opportu-nity to investigate the kinetic mechanisms. The use of surrogate fuels can contribute to theunderstanding of underlying processes such as vaporization, mixing, ignition and pollutantformation of the complex fuels [31]. In order to determine the ideal surrogate fuel componentor a mixture of components it is important to specify the targets, or what quantity needsto be predicted, like fuel properties or combustion characteristics. An overview of possiblesurrogate fuel components for practical gasoline and diesel systems or for application in mod-eling, can be found in [32] and [31]. A summary of the information can be found in tabel 4.3,together with the temperatures at which each of the components boils. These boiling pointsshow a reference to the gasoline and diesel fuels. Diesel, for example, has a boiling range of453-703 K, while gasoline has a significantly lower boiling range, viz. 303-473 K [33]. Anotherremarkable thing is the high relevance of Toluene with all the target fuels and information.This is also due to the fact that Toluene has been extensively studied and received a greatamount of modeling attention [31].

Surrogate component Chemicalformula

Gasoline Diesel Thermo-physical

Boilingpoint [K]

n-Heptane C7H16 + - + 371.6n-Decane C10H22 - - + 447.3n-Dodecane C12H26 - - + 489.5n-Hexadecane C16H34 - + - 560.02,2,4-Trimethylpentane(iso-Octane)

C8H18 + - - 372.4

2,2,4,4,6,8,8-Heptamethylnonane(iso-Cetane)

C16H34 - + - 513.2

Toluene C7H8 + + + 383.8Ethanol CH5OH - - + * 351.5

Table 4.3: Surrogate components for evaluation of gasoline, diesel and thermo-physical prop-erty information. A plus sign (+) shows a good agreement, a minus sign () shows a limitedagreement. (*Only applicable to gasoline.)

There is one property which is applicable to almost all the considered fuels: they are in aliquid state at atmospheric conditions. In order to combust the fuels in the co-flow diffusionburner, the fuels need to be evaporated.

27

4.2 Evaporation concepts

4.2.1 Evaporation principles

In both the experiments of Smooke and Long and the Burke-Schumann model, described inthe previous sections, gaseous fuels are used in the evaluations. Using liquid fuels, as is thecase in automotive fuels or bio-fuels, requires a different approach to supplying these fuels tothe burner. Since the concept of the burner and the measurement topics are supposed to bein the line with the previous experiments of Smooke and Long, the fuel supply is prescribedas a gas phase. To examine a laminar diffusion flame it is required to have a separate supplyof fuel and oxidizer in a steady flow. This implies the liquid fuel has to be evaporated, afterwhich the vapor is supplied in a steady stream. Evaporation occurs when the molecules ofthe liquid have sufficient kinetic energy to overcome the intermolecular forces which bond themolecules in the liquid phase and starts near the surface of the liquid [34]. The evaporationof liquids is dependent on the properties of the fluid, e.g. the boiling point, the ambientpressure and the temperature of the liquid. Practically, the liquid fuels are chosen for the ex-periments and so its properties are fixed, leaving the pressure and temperature as a variable.A certain temperature increase combined with a sudden pressure release, created by a throt-tle, might give a possibility to evaporate the hydrocarbon fuels, but in that case considerablepressure differences have to be introduced. Since the system pressure of the experiment isalso a variable, the use of pressure differences to evaporate the fluid is far from ideal. Fur-thermore, the control accuracy of the flows might give problems, since flow rate is in theorder of grams per hour. For these reasons, the ambient pressure variable to evaporate thefuel is discarded immediately. As a consequence the temperature is left as the best possiblevariable for evaporation. If the temperature is increased, the kinetic energy of the moleculesin the liquid fuel will increase and at a certain temperature the fuel starts to vaporize. In amulti-component hydrocarbon fuel, like automotive fuels, the lightest components of the fuelwill tend to evaporate first, due to their low boiling points. In case of a single componentfuel, decomposition or cracking may occur when the temperature is increased. The thermaldecomposition converts the large hydrocarbon molecules into a mixture of smaller molecules,of which each molecule has its own boiling point [35]. These two phenomena have to beprevented as much as possible to create a representative fuel vapor flow for the experiments.

In many evaporation systems used in existing experimental or commercial installations, aninert gas is used as an carrier gas. To evaporate small amounts of liquid, bubbler systems areregularly used. These systems run the carrier gas through a heated reservoir filled with a liq-uid which has to be evaporated. The liquid tends to evaporate as soon as it contacts the gas.The bubbles formed in the tank contain a mixture of the carrier gas and evaporated liquid.This evaporation method is hard to apply to the vaporization of multi-component liquids.Due to the range of boiling points of the components in such a liquid, the components withthe lowest boiling points will start to vaporize first and leave the components with the highboiling points in liquid phase. The risk of having such a distillation process while runningan experiment is far from ideal and therefore this concept is discarded.

4.2.2 Hot plate evaporator

A concept which is fairly comparable to the bubbler system is a hot plate evaporator. Themain difference is the method of liquid supply. While the bubbler system has a heated reser-

28

voir, the hot plate or spray evaporator has an external reservoir and the liquid is inserted inthe module through a hypodermic (hollow) needle. The spray from the needle hits a heatedplate inside the evaporator which will vaporize the liquid. Similar to the bubbler system, acarrier gas will transport the vapor out of the evaporator. To avoid cooling the evaporatedfluid, the carrier gas is preheated. An example of a hot plate evaporator is the module ofVranos [36, 37], see figure 4.1, which is used to investigate the decomposition of vaporizinghydrocarbons with a high boiling point, for instance hexadecane. The evaporator was en-tirely made out of copper, except for the fuel supply tube, and the internal surfaces wherenickel platted. The latter was done to avoid deposits of solid residues on the heated plateas much as possible. Unfortunately, deposits were observed during the course of testing [37].This might be a drawback of using such an evaporator to produce a steady vapor flow. Onthe other hand, the investigations of Vranos conclude that the fraction of decomposed fuel issignificantly small if the temperature of the carrier gas is sufficiently high [37], which meansa representative fuel vapor can be created.

Figure 4.1: Two sectional views of the hot plate evaporator of Vranos [36,37].

Another example of a hot plate evaporator is the module of Stobakk, see figure 4.2, which isconceptually similar to the one of Vranos. The fuel is injected by a needle into a box whichis heated from underneath by a heated plate and all the way around by heating tape. Apre-heated carrier gas is used to pressurize the fuel line via a by-pass and simultaneouslytransporting the vaporized fuel to the exit of the evaporator. In the investigations of Sto-bakk, a counterflow burner is connected to the evaporator and is used for flame extinctionmeasurements. In their measurements, they used heptane, two component fuels and dieselfuel. The latter fuel gave problems due to high temperatures required in the evaporator,because some materials of the evaporator could not resist such temperatures. On the otherhand, contrary to the findings of Vranos, they claim that all the components of the fuel areuniformly evaporated and no heavy components, deposits, are left in the evaporator.

29

Figure 4.2: The hot plate evaporator design of Preben Stobakk [38].

4.2.3 Controlled evaporator mixer

A different concept to vaporize liquid in a carrier gas stream is obtained by a mixture vapor-izer. In this concept, the liquid and carrier gas are mixed before both the fluids are heated.This mixing process can be controlled precisely, which results in an accurate mixture com-position, which consists of liquid droplets mixed in the carrier gas. After the mixing process,the mixture is externally heated, which vaporizes the droplets. An example of a mixturevaporizer is the controlled evaporator mixer, or short CEM, of the company BronkhorstHigh-Tech, which is also a supplier of mass flow controllers. The CEM module, see figure4.3, can be divided into a mixing part, on the top side, and a heating part, at the bottomside of the module.

The mixing part mainly consist of a control valve and a liquid and gas connection. The con-trol valve is able to restrict and control the liquid flow. The restriction is achieved by a smallorifice, with a diameter of about 100 m, which can be closed by a plunger. The plungeris spring loaded and naturally closed. A electric magnetic force is able to open the plunger,which causes the liquid to flow through the orifice. The mass flow of the liquid is measuredupstream and by adjusting the magnetic force of the valve, the flow can be controlled. Whenthe liquid is able to pass the orifice, it will be cut of in small droplets by the carrier gas flow,which is entrained just underneath the orifice. This process creates a mixture of dropletsand carrier gas. If the carrier gas mass flow is also measured and controlled, a very accuratemixture can be created. After the mixing process the mixture is forced to flow to the heatingpart of the module. The heating part consists of a spiral which is casted in a solid metalblock and is externally heated. The mixture of liquid droplets and carrier gas flows throughthe spiral and heats up. If the temperature of the heated block is sufficient, the droplets inthe mixture will vaporize. This process results in a stable and accurately controllable vaporflow. The main drawback related to the liquids considered for the experiments regarding au-tomotive fuels, is the limited temperature of the CEM module. Due to prevention of meltingthe metal block, the temperature of the module is restricted to a maximum of 483 K.

30

Figure 4.3: A schematic lay out of a Controlled Evaporator Mixer.

4.2.4 Capillary force vaporizer

Like stated before, the physical properties of the fluids considered for the experiments arefixed, but the majority of the properties are dependent on temperature, especially when aphase change is taken into account. Two important properties depending on temperatureare density and viscosity. The capillary force vaporizer (CFV), of the company Vapore, usesthese property changes when a liquid phase transforms to a gas phase. The CFV moduleconsists of three different, specially engineered, ceramic disks: an insulator, a vapor gen-erator and an orifice disk, see figure 4.4. The insulator disk, at the bottom, is in contactwith the liquid and consists out of a porous material, which is able to draw the liquid outof its reservoir. The vapor generator disk, in the middle, consist of very high porosity andexceptionally small uniform pores. The orifice disk is fixed on top of the vapor generator diskand is able to collect the vapor which exits the pores. Power to deliver heat for evaporationcan be supplied from the top of the orifice disk and can reach down to the vapor generatordisk by thermal-mechanical conduction or electric resistance.

31

Figure 4.4: A schematic lay out of a Capillary Force Vaporizer [40].

The capillary force vaporizer, like the name already suggests, uses the capillary pressure of aliquid in a porous solid. The two driving forces behind this pressure are the force of adhesionbetween the molecules of a liquid, which is responsible for the surface tension, and the forceof adhesion between the liquid molecules and the surface of the solid [39]. The capillarypressure is reversely proportional to the diameter of the pores, which implies a decrease ofthe diameter, causes an increases of the pressure. In the vapor generator disk, the exter-nally applied heat causes the liquid to vaporize and so the density and viscosity of the fluidchanges. The viscosity of the gas phase of a fluid is lower than that of its liquid phase, butthe difference in density is many times higher. This implies the vapor flows easier throughthe pores than the liquid, but at an equal mass flow, the vapor requires significantly morevolume. As a consequence the vapor must have a higher velocity than the liquid at an equiv-alent mass. As a result the porous material hinders the vapor flow such that the pressure willincrease. In the end, the vapor will escape through the center aperture in the orifice disk withvelocities which can reach the speed of sound. In this way, the capillarity force vaporizer isable to vaporize any liquid, so also the considered automotive fuels. The main disadvantageis that one CFV module is only capable to supply certain mass flows at certain pressuresand temperatures for one certain liquid. A balance between capillary pressure, porosity andthickness of the ceramic disks and heat supply must be made for determining the mass flowand pressure for each type of liquid.

4.3 Evaluation of evaporation concepts

In the previous section, three different evaporation devices were introduced. One thing thatthese three devices have in common, is the requirement of heat to create the vapor. The maindifference between the devices is the way of increasing the liquid surface, so it will vaporizeeasier and require a lower temperature than when the liquid is in a reservoir. The hot platevaporizer uses a spray to increase the surface, the CEM module uses a special mixing process

32

to create droplets and the CFV module uses extremely small pores. The method of supplyingheat is also different, but is mainly done by external heating elements shaped to fit withinthe device. To evaluate the devices to conclude which device is best applicable to the systemfor the experiments, a number of criteria has been set up. The first criterion is the capabilityto vaporize the fuels with a high boiling point, requiring high temperatures for evaporation,which might give problems to the materials inside the devices. The second criterion is theguaranty of a fair vapor quality and purity, which creates a representative vapor flow for theexperiments. A representative vapor flow implies that the chemical structure of the vapor isequal to the structure at liquid phase. Deposition of heavy components of the fuel on partsof the device, creating solid residues, or decomposition of the fuel due to high temperaturecracking, might destroy the chemical structure, which has to be prevented. The third cri-terion is the possibility to accurately control the mass flow which can easily be reproduced.This to control the experiments and be able to reproduce results. The fourth criterion isreferring to the possibility to use the device in a pressurized environment, required for theexperiments. The devices have to withstand elevated pressures and operating experience inthese environments might be of great value. The last condition is not the least importantone: the availability of the devices. Can the components of the device be delivered from shelfor does it have to be designed and constructed? Table 4.4 shows an overview of the criteriaand gives a comparison between the three devices.

From this comparison, a choice of the evaporator device have been made. Due to the re-producible and accurate mass flows which can be created, the experience in high pressureenvironments and the good availability of the device, the controlled evaporator mixer is cho-sen as the definite concept for vaporizing the fuel in the experiments. The only drawback isthe limit of the maximum temperature, which gives problems when when fuels are consid-ered with high boiling points. A solution is described in the next section, which gives alsoan overview of the whole vapor supply system.

4.4 Final evaporation concept

In the previous section, a definite evaporation concept has been chosen. From the threeoptions, the controlled evaporator mixer is the best option applicable for the experiment.However, there is one issue which has to be taken into account. The module has a limitedmaximum temperature of 483 K, which is too low to evaporate the components in the au-tomotive fuels with a high boiling point, such as hexadecane (C16H34), which has a boilingpoint of 560 K. This issue is solved using the partial pressure of the carrier gas which ismixed with the liquid or the vapor pressure of the fuel in the mixture. The higher the par-tial pressure of the carrier gas, the more the liquid droplets are surrounded by the gas, theeasier the molecules can escape from the liquid. If the mixture of liquid and carrier gas issufficiently heated, the liquid will be entirely vaporized. To determine the partial pressure,the maximum vapor pressure of the liquid at the adjusted temperature of the evaporator isrequired. Figure 4.5 shows a vapor pressure chart of a range of hydrocarbon fuels. In everypoint above the line of a fuel, the fuel is in a liquid phase and in every point below the lineit is in a gas phase. From this chart the partial pressure of a fuel pf can be determined at agiven temperature. Together with the total pressure of the fuel and carrier gas mixture, thefuel mole fraction can be determined by:

33

Hot plate evap-orator

Controlledevaporatormixer

Capillary forcevaporizer

Mass flow range[g/h]

Flexible (depend-ing on design)

0.0015 - 1200 5 - 250

Capability tovaporize fuelswith high boilingpoints

High temper-atures requirespecial materialsin the construc-tion

Limited maximumtemperature (483K); measures haveto be taken to va-porize heavy fuelcomponents

Device is able tovaporize all auto-motive fuels

Quality/purity ofthe vapor

Quality debatabledue to chancesof deposition ofsolid residues andhigh tempera-tures stimulatedecomposition

The restrictedtemperature re-duces the chanceof decomposition;the device has ahigh reproducibil-ity

Creates a pure va-por flow due tothe thermal bal-ance of mass flowand pressure

Controllabilityand accuracy ofmass flow(s)

Flows can becontrolled by ac-curate mass flowcontrollers

Equal to the hotplate evaporator

Mass flow is abalance of poros-ity and tempera-ture of the module

Possibilities to op-erate in high pres-sure environments

Possible, but thereis no experiencein pressurized en-vironments

Great experiencein pressurizedenvironments,using pressurecontrollers

Applicable in lim-ited pressurizedenvironments,but is depen-dent on moduleconfiguration

Availability of thedevice

Device has to bedesigned and con-structed

Device can bebuild out of di-rectly availablecomponents

Modules are tem-porarily not avail-able

Table 4.4: Comparison between the three evaporator devices

Xf =pfpt, (4.1)

where pt is the total pressure of the mixture. For example, if hexadecane as fuel is consideredand the maximum evaporator temperature is limited to 473 K, the vapor pressure of thefuel is maximum 0.075 bar, according to figure 4.5. This means, if the system is operated atatmospheric pressure (1 bar), the mole fraction fuel Xf is 0.075, since Xfuel = pf/pt. Themole fraction of the carrier gas is determined by: Xgas = 1Xf . Now that the mole fractionsare determined and the mass flow of the evaporated fuel and carrier gas mixture is known,the mass flow fuel can be calculated using:

f = tXfMfM

, (4.2)

34

273 323 373 423 473 523 573 623 673103

102

101

100

101

102

Temperature [K]

Pres

sure

[bar

]

C2H6C4H10C6H14C8H18C10H22C12H26C14H30C16H34C18H38C20H42

Figure 4.5: Vapor pressure chart of a range of hydrocarbons [41].

where f and t are the mass flow of respectively the fuel and the total mixture, Mf is themolar mass of the fuel and M is the mean molar mass of the fuel and carrier gas mixture.

The mass flows in the evaporator system are measured and controlled by mass flow controllers,while the pressure of the system is controlled by a pressure controller. Figure 4.6 shows aschematic overview of the experiment, focused on the vapor supply. The liquid fuel is storedin a membrane accumulator (2 liter) and is pressurized by the carrier gas of which the pressureis controlled by a pressure controller. Before the mass flow of the fuel is measured the liquidis first filtered by an inline filter, with a pore size of 7 m. The mixing part of the CEMmodule receives a signal from the mass flow meter and controls the flow by opening a valve.Together with the fuel, the carrier gas is introduced in the mixing part. Nitrogen is chosento function as carrier gas, as it is an inert gas in combustion, which is also in great amountavailable in air. The nitrogen is available from a gas bottle and the flow is controlled bya gas mass flow controller. For a further explanation of the construction and principles ofthe mass flow controllers and the controlled evaporator mixer, see appendix A. After theflow is mixed, the mixture is heated and the liquid fuel will vaporize in the heating spiral.After the fuel is vaporized, the vapor can be supplied to the high pressure burner. Betweenthe CEM module and the burner, the vapor has to be kept at a temperature of at least thetemperature adjusted on the CEM module. This is done via a flexible heated hose, whichis a highly insulated hose containing a flexible tube surrounded by a heating element and isable to deliver a maximum power of 110W. To minimize the distance the vapor has to travelbefore reaching the burner, while maintaining as much as flexibility as possible, the lengthis compromised to be 1 meter. The inner diameter of the hose is 4 m