Heat transfer of oxy-fuel flames to glass : the role of chemistry and radiation Cremers, M.F.G.

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1 Heat transfer of oxy-fuel flames to glass : the role of chemistry and radiation Cremers, M.F.G. DOI: /IR Published: 01/01/2006 Document Version Publisher s PDF, also known as Version of Record (includes final page, issue and volume numbers) Please check the document version of this publication: A submitted manuscript is the author's version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website. The final author version and the galley proof are versions of the publication after peer review. The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication Citation for published version (APA): Cremers, M. F. G. (2006). Heat transfer of oxy-fuel flames to glass : the role of chemistry and radiation Eindhoven: Technische Universiteit Eindhoven DOI: /IR General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. Users may download and print one copy of any publication from the public portal for the purpose of private study or research. You may not further distribute the material or use it for any profit-making activity or commercial gain You may freely distribute the URL identifying the publication in the public portal? Take down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. Download date: 11. Nov. 2018

2 Heat Transfer of Oxy-Fuel Flames to Glass: The Role of Chemistry and Radiation PROEFSCHRIFT ter verkrijging van de graad van doctor aan de Technische Universiteit Eindhoven, op gezag van de Rector Magnificus, prof.dr.ir. C.J. van Duijn, voor een commissie aangewezen door het College voor Promoties in het openbaar te verdedigen op woensdag 7 juni 2006 om uur door Marcel Franciscus Gerardus Cremers geboren te Venray

3 Dit proefschrift is goedgekeurd door de promotor: prof.dr. L.P.H. de Goey Copromotor: dr. K.R.A.M. Schreel Dit proefschrift is mede tot stand gekomen door financiële bijdrage van Philips Lighting B.V. Copyright c 2006 by M.F.G. Cremers All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form, or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior permission of the author. Cover design: Paul Verspaget Paul Verspaget Carin Bruinink Grafische Vormgeving - Communicatie Cover photo: Heating lamp glass with oxy-fuel burners Copyright c by Philips Lighting B.V. Printed by PrintPartners Ipskamp B.V.. A catalogue record is available from the Library Eindhoven University of Technology ISBN-10: ISBN-13:

4 To my parents and sister

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6 Contents 1 General introduction Background Problem Definition Objectives Deliverables Scope of the Thesis Heat transfer of a chemically reacting stagnation flow to an object Heat transfer in a glass object From heat transfer predictions towards burner design Outline of the thesis Chemically reacting stagnation flow General introduction Stagnation flow Flame chemistry Stagnation layer chemistry Gas radiation Governing Equations Conservation Equations Equations of State Diffusion Models and Transport Coefficients Gas Chemistry Boundary conditions Inlet Boundary Conditions Stagnation Plane Boundary Conditions This thesis Assumptions Equations Computational strategy

7 vi Contents 3 Heating of glass objects General introduction Chemical and thermodynamic properties Optical properties Governing Equations Energy Conservation Equation Radiation Boundary Conditions This thesis Assumptions Equations Computational strategy Heat transfer mechanisms of laminar flames of hydrogen+oxygen Introduction Governing equations Time scale analysis of the stagnation flame Time scale analysis for the quartz glass product Heat transfer of a non-reactive stagnation flow Heat transfer of a reactive stagnation flow Chemical equilibrium Surface chemistry Conclusions Thermochemical heat release of laminar stagnation flames of fuel+oxygen Introduction Conservation equations and boundary conditions Spatial analysis of the stagnation flame Flame front Thermal boundary layer Equilibrium zone Chemistry in the stagnation boundary layer Conclusions Integrated radiative transfer equation for gray and non-gray media Introduction Theory Conservation equations Boundary conditions Discretization Solution of the integrated RTE for a spectral band Discussion A model problem: heat flux inaccuracies

8 Contents vii The radiative source term Practical situations Conclusion From heat transfer predictions towards burner design Introduction Fuel gas Thermochemical heat release Radiative heat loss of a glass plate General conclusions Chemically reacting stagnation flow Heat transfer in a glass object From heat transfer predictions to burner design A Gamma-functions 115 B Tables 117 B.1 Blackbody fractions Bibliography 119 Summary 129 Samenvatting 131 Curriculum Vitae 133 Dankwoord 135

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10 1 Chapter General introduction 1.1 Background The first practical electrical lamp was the incandescent lamp produced by Thomas Edison in Edison used a glass light bulb with a thin carbonized cotton sewing thread as filament material. This was the starting point for the development of electrical lamps for many purposes. Today, lamps are used in many devices and environments, which has led to thousands of different lamp types. Typical applications are household appliances, automotive applications, office and industrial lighting, theatre and arena lighting, road and airport lighting, etc. Most of the lamp types can be placed within one of the categories [99]: incandescent, tungsten halogen, fluorescent, mercury, metal halide, and sodium lamps, and are available in a variety of shapes and sizes. These lamps are filled with a gas at low, ambient or high pressure. Fig. 1.1 shows a schematic representation of an incandescent lamp. The main production steps for most lamp types are shaping the outer bulb, globe or tube, if needed implementing the high pressure glass core element, fixing the electrical components, evacuating the air and adding the fill gas, and fixing the neck and base elements. These steps can be divided in many substeps, which have to be performed in order to produce a lamp. In many of these steps, the glass is melted locally by means of flame impingement, and a variety of glass types is used. The most important requirement of the glass used in electric bulbs is to form a transparent envelope around the light source, i.e. the emission of light of the filament or charged gas [104], or alternatively allow deposition of a coating which transforms the light emitted by the gas into visible light. Depending on the required optical properties of the glass, and on the pressure and temperature inside the lamp, the glass can be a soft glass, hard glass or even quartz glass, which has a high melting temperature of around 2000 K. In order to reach the high melting temperatures, often flames are used based on mixtures of a fuel and pure oxygen, commonly refered to as oxy-fuel mixtures. These flames possess a high flame temperature, together with a high flame speed. As a result, the energy throughput is high, and so is the heat transfer rate of these impinging oxy-fuel flames to the products. Oxy-fuel burners are not only used for heating parts in the production process of a lamp, but also for many other purposes. Many industrial heating processes use pure oxygen or oxygen-enriched air as oxidizer for combustion. Typical applications

11 2 General introduction Filament Bulb Fill Gas Lead-In Wires Stem Press Support Wires Exhaust Tube Base Insulating Disc Figure 1.1 Representation of the incandescent lamp and its parts. are metal heating, melting and calcining [6]. Baukal [6] shows that oxygen-enriched combustion is prefered in processes that demand a high flue gas temperature, processes that need a high heat transfer rate to achieve high thermal efficiencies, processes that need a high throughput and high product quality by heating a limited volume, and processes that have a limitation on NO x emissions. The adiabatic flame temperature of a stoichiometric CH 4 -O 2 -flame is over 3050 K and is much higher than the adiabatic flame temperature of a CH 4 -air, which equals 2223 K [6]. The laminar burning velocity of a stoichiometric CH 4 -O 2 flame is 3.1 m/s and that of a stoichiometric CH 4 -air flame is 0.36 m/s [11]. The high flame temperature together with the high flame speed, result in high heat transfer rates, which can be applied locally in order to heat a limited volume. Furthermore, if no nitrogen is present in the fuel or oxidizer, formation of NO x is absent. However, due to mixing with surrounding air, together with the high flame temperatures, formation of some NO x can hardly be prevented in practice. Switching from a laminar to a turbulent oxygen-fuel flame in an ambient environment increases the mixing with nitrogen species from the surroundings significantly and leads to an increase of NO x emissions. For reasons of NO x emissions and for safety reasons oxy-fuel burners should be handled with care. 1.2 Problem Definition Premixed, non-premixed and partially premixed burners are used in the different stages of the lamp production process of many lamp types, of which the traditional incandescent lamp is probably best known. Fig 1.1 shows a schematical representation of such a simple incandescent bulb, with the different components. Based on the practical experience of glass technicians these burners are tuned by hand in order to

12 1.3 Objectives 3 Unburnt Gas Burnt Gas Dn δ f D H y, v x, u Figure 1.2 Nozzle Exit Flame Front Tube Shell Schematical burner set-up with a premixed flame impinging a tube. optimize the efficiency of the production process. There are several problems associated with this practice. The main problem is that the development of a production process of a new lamp type is an extensive and time-consuming task. The burner type, type of fuel gas, and burner set-up is often chosen on a subjective basis. As a result, the cycle times when developing a new lamp making process are relatively long. Then, the change-over times are relatively long when a production line has to be adapted for the production of another lamp type. For both new and adapted production processes, it is not known if the chosen set-up is the optimal set-up, and further optimization is often desired. Optimization is mostly explained in terms of process speedup, increasing process stability, and increasing production flexibility. Furthermore, the controllability and efficiency of the lamp production process needs to be improved. In many cases, the production process can be optimized, but the optimization is an elaborate task and is difficult to verify. To optimize this process at Philips Lighting B.V. a research project has been started. This project is a joint research effort of Philips Lighting B.V. and Eindhoven University of Technology, to study the heat transfer of impinging oxy-fuel flames to (quartz) glass products, by performing an in-depth study on the heat transfer phenomena involved in the heating of an object. 1.3 Objectives Optimization of the production process can only be achieved if there is a clear knowledge of the process of heating a (quartz)-glass product with oxy-fuel flames in

13 4 General introduction an impinging-like configuration. A schematic representation of a flame impinging a product is given in Fig Different physical phenomena influence the heat transfer rate. The different phenomena that are identified and expected to be of major importance are [9], stagnation flow characteristics, chemistry in the flame front, chemistry in the stagnation boundary layer, gas and glass radiation. The focus is to model, quantify, and validate these phenomena. The main objective of the research is to investigate the importance of the heat transfer phenomena on the total heat transfer process, and see how each phenomenon is affected by physical and chemical parameters, like strain rate, temperature or mixture composition. 1.4 Deliverables Conclusions have to be drawn on the qualitative effect of changes in the set-up on the local heat transfer, in order to optimize the heat transfer process, which can be used as a guideline to optimize the production process of a lamp. In the previous section, a coupling was made between the heat transfer phenomena and the physical parameters that affect each heat transfer mechanism. Now it is important to find a coupling between the production process and the physical parameters. Therefore, heat transfer predictions for burner design are needed. These predictions show how changes in the set-up influence the physical parameters, and hence influence the heat transfer rates. The heat transfer predictions help the operator to choose a burner type and fuel gas for a particular production step, reduce the process development cycle times, and reduce the number of burner types. Heat transfer predictions for burner design include the effect of e.g. burner geometry, distance from burner to the product, and fuel gas, on the physical parameters, like strain rate, temperature or mixture composition. Then, based on the fundamental research, guidelines should be given on how a change of a physical parameter influences the different heat transfer phenomena and as a result the total heat transfer rate. 1.5 Scope of the Thesis One of the most complicated steps in the production process of a lamp is when a small volume of the glass object has to be heated to a high temperature in a short period of time. Then, high local heat transfer rates are needed with relatively small

14 1.5 Scope of the Thesis 5 flames that possess a high flame temperature and high flame velocity. Therefore, flames based on mixtures of a fuel and pure oxygen are used. The diameter of the nozzle exit is relatively small, and as a result, the flames are laminar. To increase the heat transfer rate even more, the flame tip is placed close to the object surface. Quartz glass is chosen as solid material, because this glass type has a much higher melting temperature than many other glass types, and therefore requires the highest heat transfer rates. In section it is shown that a one-dimensional approximation of the flow, chemistry and thermodynamics is expected to be a fair representation of the real three-dimensional problem. Therefore, a one-dimensional numerical study is conducted to determine the heat transfer from premixed laminar oxy-fuel stagnation flames to quartz glass products. Furthermore, the products considered, often have a tubular shape with a radius much larger than the shell thickness. As a result, a one-dimensional infinite plate is the considered geometry for the glass object. The research is mainly conducted within two PhD-projects. M.J. Remie mainly focusses on the influence of flow phenomena on the heat transfer rates, which will be presented in a seperate thesis. The results presented in this thesis discuss (1) the effect of flame chemistry and chemistry in the stagnation boundary layer on the heat transfer rate of a chemically reacting stagnation flow to an object, (2) the effect of radiative heat transfer on the heating process of a glass object. The chemically reactive stagnation flow and the object are treated seperately throughout the thesis. This is allowed because the heating time scale of the glass plate is much larger than the heating, transport and chemical time scales of the chemically reacting flow. The typical heating time scales of the stagnation flow and object are determined and outlined in chapter Heat transfer of a chemically reacting stagnation flow to an object Extensive research has been undertaken by various researchers on the heat transfer of stagnation flames to products. Most studies, however, are semi-analytical derivations of stagnation point heat transfer rates, of inert and reactive hot gases to objects. In most of these studies, flame calculations are not performed, and the effect of chemistry in the boundary layer on the heat transfer rate is taken into account by means of enthalpy differences. On the other hand, the stagnation flame calculations with complex chemistry calculations are usually based on mixtures of a fuel and air. Results of stagnation flames based on oxy-fuel mixtures with complex chemistry calculations are very scarce. Therefore, an extensive study, with full chemical calculations, is undertaken in order to determine the heat transfer of oxy-fuel stagnation flames to objects. A non-reacting hot gas impinging an inert surface is taken as the basic problem, and is currently under investigation. For this problem, analytical solutions can be derived, and the heat transfer rates can be estimated, see e.g. [110]. When flame

15 6 General introduction chemistry and stagnation layer chemistry is taken into account, the heating process of the product is affected significantly, and the question arises how these phenomena influence the heat transfer process. First, flame chemistry is studied by comparing a hydrogen-oxygen and a hydrogenair mixture. Since heat transfer is largely determined by typical flame speeds and adiabatic flame temperatures, flame speeds and temperatures for both mixtures are determined with different complex reaction mechanisms in chapter 4. Flame speeds and temperatures for oxy-fuel mixtures with acetylene, propane and butane as fuel gas are given in chapters 5 and 7. Second, dissociated species in the burned gases enter the cool stagnation layer and may recombine exothermally into stable products, releasing heat and boosting the heat transfer. This process is also called thermochemical heat release (TCHR). When the flame is far from the object, the flue gases will reach chemical equilibrium before they enter the stagnation boundary layer. Then, the equilibrium composition of the burned gases consists mainly of decomposed species, even if the initial oxy-fuel composition consisted of higher alkanes, and a relatively simple reaction mechanism can be used to calculate the recombination chemistry near and at the surface. In chapter 5 it is shown under which conditions chemical equilibrium is reached. The effect of recombination in the stagnation boundary layer is studied for a H 2 -O 2 -mixture in chapter 4 and for different C x H y -mixtures in chapter 5. If the stagnation layer is not in chemical equilibrium, surface reactions may enhance the heat transfer rate even further. The effect of recombination reactions on the total heat transfer rate directly at a surface, by imposing a chemically active Platinum surface, is discussed in chapters 4. Third, the effect of the local strain rate on the total heat transfer rate is investigated. The local strain rate is a typical parameter of the flow, and is directly coupled to the local velocity gradient. An analytical approximation for the heat transfer coefficient is derived for a non-reacting stagnation flow with negligible viscosity in the sublayer. The effect of the strain rate on the heat transfer coefficient is incorporated in the approximation. The heat transfer coefficients calculated with this approximation are compared with heat transfer coefficients determined numerically for stagnation flows with and without recombination in the stagnation boundary layer, see chapter 4. The effect of the strain rate on the ability of the flue gas to reach chemical equilibrium before entering the stagnation boundary layer is investigated in chapter 5, while the effect of the strain rate on the addition of TCHR to the total heat transfer rate is outlined in chapter Heat transfer in a glass object The glass object is heated by a stagnation flame. At low temperatures, the main heat transfer mechanism inside the glass is conduction. Once the object reaches a higher temperature, radiative heat transfer becomes an important heat transfer

16 1.5 Scope of the Thesis 7 mechanism. Heat transfer by radiation redistributes heat inside the object, and is the dominant heat loss mechanism from the object to the surroundings. The heat losses have to be determined in an adequate way to simulate the heating process accurately. The temperature gradients inside the product have to be determined accurately to know the thermal stresses. Determining the heat transfer in a glass object is a combined conduction-radiation problem. A glass is a semi-transparent medium, and spectral solution techniques have to be applied to determine the radiative heat transfer rates accurately. With the traditional solution techniques, if the medium is semi-transparent and internal temperature gradients are high, significant inaccuracies have to be allowed when the heat fluxes are calculated on the same course grid as the conductive fluxes. Chapter 6 shows a new spectral band formulation with which the radiative heat fluxes can be determined accurately on a course grid with large temperature gradients. The new method is applied to a combined conduction-radiation problem. First it is assumed that the medium has optical properties that are independent of wavelength, i.e. a gray medium. The effect of the gray absorption coefficient on the typical heat loss, temperature gradient and cooling time scale is investigated. Then a medium with semi-transparent optical properties is considered, consisting of one almost completely transparent spectral band for short wavelengths, and one almost completely absorbing spectral band for long wavelengths and which is a typical optical property for glass. The transition from the transparent to the absorbing band occurs at a cutoff wavelength. The position of the cutoff wavelength can be very different for different glass types. Therefore, the effect of the position of the cutoff wavelength on the typical heat loss, temperature gradient and cooling time scale is also investigated From heat transfer predictions towards burner design The different heat transfer phenomena will be studied from a fundamental point of view throughout the main part of the thesis. Based on this fundamental knowledge, some predictions will be presented in chapter 7. These predictions show how changes in the set-up influence the physical parameters that determine the heat transfer rate. It should be noted that the influence of flow phenomena will mainly be treated by M.J Remie in a seperate thesis. In this thesis we will focus on how the chosen fuel gas determines the flow velocity of the burned mixture, the sensible and chemical enthalpy of the burned mixture, and the maximum strain rate how the chosen fuel gas, and C/H-ratio, determines the heat flux ratio including TCHR and without TCHR how the maximum temperature of a glass plate can be estimated if the optical properties of the glass are known.

17 8 General introduction 1.6 Outline of the thesis The chemically reacting stagnation flow, and the heating of the glass object are treated more or less seperately throughout this thesis. Chapter 2 discusses the theory of a stagnation flow, including a summary of the different physical and chemical phenomena that are present in a reacting stagnation flow, the governing equations and boundary conditions in vector notation, and the equations in one-dimensional form as used in the remainder of this thesis. Chapter 3 discusses the theory of solid object heating, including the thermodynamic and optical properties of the solid, the governing equations and boundary conditions for the solid, and a detailed discription of radiative heat transfer inside a semi-transparent medium. Chapters 4, 5 and 6 discuss the main findings and results extensively. Chapter 4 and 5 treat the phenomena in the chemically reactive stagnation flow, and Chapter 6 treats radiative transport in a solid material. These chapters are reprints of submitted, accepted or published articles. Chapter 7 shows how some of the heat transfer predictions can be applied for burner design. The thesis ends up with general conclusions and a summary.

18 2 Chapter Chemically reacting stagnation flow This chapter discusses the theory of a chemically reacting stagnation flow impinging against an object. In section 2.1 a general introduction is presented of different physical and chemical phenomena in a chemically reacting stagnation flow. In section 2.2 chemically reacting stagnation flow equations are presented in vector notation, and section 2.3 presents the corresponding boundary conditions. Finally, in section 2.4 it is shown that the flow can be approximated by a one-dimensional problem, and the one-dimensional equations that are used in the remainder of this thesis are given. 2.1 General introduction In this section a discription is given of a stagnation flow, flame chemistry, stagnation boundary layer chemistry and gas radiation, and how these phenomena may influence the heat transfer Stagnation flow Both laminar and turbulent flames are often used in industrial heating processes. Turbulent flames are mostly used when the combustion mode is of the non-premixed type and intense mixing is needed to enhance combustion, for example in industrial ovens, aviation jet turbines and compression ignition engines. On the other hand, in the lamp making process, premixed high velocity burners are often used, and a schematic representation is given in Fig. 1.2 The nozzle diameter D n is small, with the Reynolds number based on the nozzle diameter and the mean velocity, viscosity, and density of the gas in the nozzle of the order of , while the Reynolds number in the flame front based on the typical stream tube width, the laminar burning velocity, viscosity and density in the flame front is of the order of As a result the flame jets studied in this thesis are considered laminar. Depending on the nozzle geometry the unburned mixture leaves the nozzle exit as a plug flow or (partially) developed flow. After combustion takes place a flame jet impinges the object. When using an impinging flame jet with flame temperatures up to approximately 1700 K forced convection is the dominant heat transfer mechanism [5, 65].

19 10 Chemically reacting stagnation flow It was understood that for these low temperature flames, the share of forced convection in the total heat transfer may be 70-90% [8, 95]. This type of flow is often called frozen flow, since no chemical reactions are involved. In that case no heat release occurs from chemical reactions near the target surface [72]. As a result, for these low temperature flames forced convection is often considered as the only heat transfer mechanism. Semi-analytical solutions for the heat transfer from stagnation flows to objects of different shapes have been studied extensively. In most of these solutions the heat transfer in the stagnation point is considered. In the original solutions, where a uniform flow impinges normally to a body of revolution, the radial flow component at the stagnation edge of the stagnation boundary layer is determined from potential flow theory and is given by, v βy (2.1) with y the distance along the body. The constant β is known as the stagnation velocity gradient, and we will later redefine it as the local strain rate K. At the edge of the stagnation zone, β is constant and equal to, β s ( ) v (2.2) y y 0,x δ e with v the velocity in radial direction y, x δ e the outer edge of the stagnation boundary layer, and y 0 a position on the centerline axis. For a one-dimensional stagnation flow, Eq. (2.2) holds for 0 y. The factor β s is also known as the surface velocity gradient [5], or the velocity gradient in the radial direction, outside of the boundary layer, in the vicinity of the stagnation point [94, 55, 105]. For a sphere, disk, and cylinder in crossflow, analytical solutions for β s have been found [66, 93]. For an axisymmetric planar jet impinging normally onto a flat plate of infinite size, the factor β s has been derived as [118], β s 3πu e 16d j (2.3) with u e the velocity normal to the stagnation plane and d j the jet width at the edge of the stagnation boundary layer. In the derivation it was assumed that the velocity far away from the stagnation plane is uniform and approximately equal to u e. From experimental studies using semi-analytical solutions, van der Meer [93] obtained a β s -value equal to β s u N /D N at small burner to plate distances, with u N the uniform velocity in the nozzle exit and D N the nozzle exit diameter. Kilham et al. [73] found for various laminar oxy-fuel flame jets impinging onto a flat plate that β s u e /d j. Sibulkin [121] derived an expression for the heat flux at the stagnation point, with an external uniform flow impinging against a body of revolution, q s β s ρ e µ e 0.5 Pr 0.6 e c pe T e T s (2.4)

20 2.1 General introduction 11 where ρ e, µ e, Pr e and c pe are the density, viscosity, Prandtl number, and specific heat capacity at the outer edge of the stagnation boundary layer respectively. Since T e is the temperature of the external flow at the outer edge of the stagnation boundary layer, and T s is the wall, or stagnation plane, temperature, the heat flux is driven by this temperature difference. Many semi-analytical solutions, see e.g. [94, 44, 113, 56, 50, 52, 24], for laminar and turbulent stagnation flows, with and without chemical reactions, are based on Eq. (2.4). In contrast to the potential flow-based and semi-analytical solutions, Remie [110] derived an analytical solution for the velocity profile of a non-reacting hot stagnation flow, impinging against a flat surface. From this profile an expression was found for the heat transfer rate in the stagnation point. This expression is written in terms of integral functions of dimensionless numbers. If viscosity in the stagnation boundary layer is neglected and the specific heat capacity, thermal conductivity and density are taken independent of temperature a simplified expression is found, see chapter 4. With this equation the influence of e.g. the local strain rate, which is dependent on the distance to the surface, on the heat transfer rate is studied, and is outlined in chapter Flame chemistry In general, combustion is the exothermic conversion of a fuel and oxidizer into products. A fuel can be a solid, a liquid or a gas. In this thesis we will focus on gaseous fuels only, because in the lamp making process only gaseous fuels are adopted. Gaseous fuels are commonly used in industrial applications, and are mostly hydrocarbons like methane or LPG. Sometimes hydrogen is added to the fuel gas and if high flame velocities are needed, hydrogen is used in its pure form. The most common oxidizer is air, which consists mainly of nitrogen and oxygen. However, when high temperatures and flame speeds are needed, often is chosen for pure oxygen as oxidizer. If the fuel and oxidizer are mixed such that a lean or stoichiometric mixture is obtained, a premixed flame converts the fuel gas to products where the chemical reactions take place within a thin flame front. Different inlet mixtures lead to different flame chemistry, and as a result to different laminar flame speeds and adiabatic flame temperatures. The laminar flame speed is determined by the typical diffusion velocity of the species in the mixture and the typical reaction times. If the fuel and oxidizer are separate streams a flame front is formed at the position where the fuel and oxidizer stream meet, leading to a non-premixed flame. The mixing is forced by diffusion. If diffusion fluxes of the fuel and oxidizer to the flame front are high, mixing is enhanced and chemical reactions develop easier, leading to a thinner flame front. In practice, the combustion system is often a combination of a premixed and non-premixed system. A configuration of multiple flame front types, premixed and non-premixed, in the same system is very com-

21 12 Chemically reacting stagnation flow mon. Bongers [10] gives a more extensive overview of the general principles in combustion sytems. Configurations in which multiple flames occur are for example premixed counterflow flames and triple flames, see e.g. Van Oijen [101]. Although in a lamp making manufacturing, a variety of flame types including premixed, nonpremixed and partially-premixed flames can be found, we will focus in this thesis only on premixed flames. Due to its high flame temperature, high flame speed, and relatively small size, this flame type is commonly used when a high local heat input is needed. The higher the flame speed, the higher the mass flux and the higher the heat transfer rate. The reacting gas possesses a chemical and sensible energy content. The sensible energy content of the inlet mixture is determined by the temperature, while the chemical energy content is determined by the initial composition. Once the inlet mixture is combusted, it reaches chemical equilibrium with corresponding high adiabatic flame temperature. Part of the chemical energy content has been converted to sensible energy by chemical reactions. The more chemical energy is converted to sensible energy, the higher the adiabatic flame temperature and the higher the heat transfer rate. In chapter 4 laminar flame speeds and adiabatic flame temperatures are determined for hydrogen-oxygen and hydrogen-air mixtures. In chapter 5 laminar flame speeds and adiabatic flame temperatures are presented for a number of hydrocarbon-oxygen mixtures Stagnation layer chemistry The stagnation point heat transfer rate of a non-reacting flow impinging against a surface is determined by the temperature difference, or difference in sensible enthalpy, between the hot gas and the cool object surface. However, the hot gas may consist of dissociated species, and recombination reactions may take place inside the cool stagnation boundary layer or at the surface. The exothermic recombination of dissociated gaseous species into stable products is then thermodynamically preferable, and leads to an increase of the overall heat transfer rate. This mechanism has often been referred to as (chemical) recombination, see e.g. [23, 56, 72, 129, 44, 47, 73, 24, 71]. It has also been called convection vivre [64, 8, 95] or aerothermochemistry [113]. In this thesis, the process will be called thermochemical heat release, after Baukal et al. [5, 3, 4]. The effect of thermochemical heat release in the total heat transfer rate becomes more important when the main stream gas contains a high concentration of dissociated species. A high concentration of dissociated species is reached at high flame temperatures. Oxy-fuel mixtures possess a relatively high flame temperature compared with mixtures based on air, and have therefore a much higher content of disscociated species. The reason for this is that mixtures of a fuel and air consist of a relatively large amount of inert nitrogen. The N 2 -species in air acts as a heat sink, which moderates the flame temperature and as a result drops the concentration of dissociated species and the effect of TCHR on the total heat trans-

22 2.1 General introduction 13 fer rate. At high gas temperatures, TCHR may be of the same order of magnitude as forced convection [4]. Two TCHR mechanisms are identified by Giedt et al. [47], known as equilibrium TCHR and catalytic TCHR. In equilibrium TCHR gas-phase chemical reactions occur in the stagnation boundary layer. Dissociated species enter the stagnation boundary layer by diffusion and convection, and have sufficient time to collide with other unstable atoms to form stable products. As long as the typical chemical reaction time is short compared to the typical diffusion time, the species recombine exothermally in the gaseous phase, enhancing the total heat transfer rate. In catalytic TCHR, diffusion of dissociated species to the stagnation plane is relatively fast compared to the chemical reaction times. Therefore, the dissociated species are not able to form stable products before they reach the stagnation plane, and the reactions may take place at the surface. Recombination may be accelerated when the surface is catalytically active. This recombination effect is therefore a heterogeneous effect. Baukal et al. [4] investigated experimentally the heat transfer from oxygen-enriched natural gas flames impinging normally onto a water-cooled disk. They compared the stagnation point heat transfer rate to a nearly noncatalytic alumina-coated, untreated and highly catalytic platinum coated disk, and found a maximum difference between the platinum-coated and alumina-coated of approximately 12%. Nawaz [100] showed that there is also a combined form of equilibrium TCHR and catalytic TCHR possible, and is called mixed TCHR. Some of the disscociated species react in the gaseous phase, while others reach the surface and react catalytically. In most studies the driving force for convective heat transfer is the difference in sensible enthalpy h S between the main flow and the gas at the stagnation plane. However, with TCHR included, the driving force is the total enthalpy difference h T of the gas flow at the edge of the stagnation boundary layer and the gas right at the stagnation plane. The total enthalpy consists of the sensible enthalpy and the chemical enthalpy h C, which is the chemical potential energy of the dissociated species. Analogeous to the sensible heat transfer equation by Sibulkin, Eq. (2.4), semi-analytical solutions have been found for stagnation point heat fluxes including equilibrium TCHR, for both laminar and turbulent stagnation flows, see e.g. [44, 113, 24, 71, 23], where the total enthalpy difference was taken as potential for heat transfer. Semi-analytical solutions of the stagnation point heat transfer rate including catalytic TCHR have been proposed by e.g. [44, 113, 71]. Furthermore, most studies are based on mixtures of a fuel and air, while TCHR is especially relevant for oxy-fuel mixtures. Also the interaction with the flame front is not taken into account. TCHR in the stagnation boundary layer and at the surface for a number of oxy-fuel mixtures is calculated with complex chemistry models, and results are shown in chapters 4 and 5. Furthermore, interaction with the flame front is investigated, and results are discussed in chapter 5.

23 14 Chemically reacting stagnation flow Gas radiation Radiation is produced by the hot flue gas and is often split in nonluminous and luminous radiation. Nonluminous radiation is produced by gaseous species that can be found in the burned gases. Among the best emitters are CO 2 and H 2 O, and are present in most oxy-fuel flames. The amount of radiation produced by the gas depends on the gas temperature and partial pressures of the emitting species. Some studies indicate the importance of nonluminous radiation, e.g. [70, 64], while in other studies nonluminous radiation was found to be very low or negligible, e.g. [47, 33]. Van der Meer [93] states that flame radiation for impinging premixed methane-air flame jets is negligible because the hot gas layer has a small thickness and very low emissivity. Purvis [106] showed that for a CH 4 -O 2 and C 3 H 8 -O 2 flame impinging normal to a surface, the addition of nonluminous radiation to the heat transfer rate from the flame to the target is negligible. Baukal [6] states that in the flame region of an oxy-fuel flame dissociated species, as OH, H and O, are present, which radiatively participate. Baukal mentions that the average absorption coefficient of the furnace gas for a methane-oxygen furnace is increased up to m 1. However, because the typical flame thickness is of the order of m, the optical thickness is typically of the order At a temperature of T 3054 K the maximum radiative heat flux is then of the order of 10 2 Wm 2, which is orders of magnitude lower than the convective heat flux. Therefore, radiative heat transfer by nonluminous radiation is not investigated in this study. Luminous radiation is produced by the soot. Soot particles radiate approximately as a blackbody, and may be an important heat transfer mechanism when liquid and solid fuels are used. For gaseous fuels luminous radiation is in general not important, except when the flames are very fuel rich. Then soot particles may be formed, leading to luminous radiation. Furthermore, diffusion flames have a tendency to form soot and produce luminous radiation. Soot is not present in high temperature premixed flames. In this study we will focus on high temperature premixed stoichiometric gaseous oxy-fuel flames, from which it can be concluded that no soot is formed, and no luminous radiation is produced. 2.2 Governing Equations In this section the transport equations are given for a chemically reacting stagnation flame. In section the conservation equations for mass, momentum, energy and chemistry are given. In section the equations of state, i.e. the gas law and caloric equation are presented, as well as the equations for the thermodynamic variables. Section gives an overview of the chemical diffusion models. Finally, a brief outline of the gas chemistry modelling is presented in section

24 2.2 Governing Equations Conservation Equations The conservation equations for chemically reacting flows can be found in many books and theses, see e.g. [10, 101, 49, 77, 135, 136]. This section expresses the conservation equations for mass, momentum, species mass fractions, and enthalpy. All equations are presented in vector notation so that they are applicable to chemically reacting flows in any coordinate system. Conservation of mass is given by the continuity equation, ρ t ρu 0, (2.5) with ρ the density, t time and u the velocity vector of the gas mixture. The equation for conservation of momentum in a multi-component gaseous or fluid flow is, ρu t ρuu Π N g s i 1 ρy i b i, (2.6) where Π is the stress tensor, Y i the mass fraction of species i and b i the external force per unit mass acting on species i. Ns g is the number of species in the gas, and for every species the species mass fraction is defined as Y i ρ i /ρ, where ρ i is the mass density of species i. The stress tensor Π consists of a hydrostatic and a viscous part corresponding to Π pi τ, with p the hydrostatic pressure, I the unit tensor and τ the viscous stress tensor. The stress tensor is determined from the kinetic theory [54], and is given by, ( 2 τ κ 3 η ) u I η ( u ( u T)), (2.7) where η is the mean dynamic viscosity of the mixture. The volume viscosity κ describes viscous dissipation due to normal shear stress and is usually neglected in flame simulations [135]. Conservation of energy is written in terms of specific enthalpy j by the enthalpy conservation equation, ρj t ρju Dp Dt q τ u Q N g s i 1 ρy i u i b i, (2.8) with q the total heat flux. The material, or convective, derivative of the pressure is given by Dp p Dt t u p. The third term on the right hand side represents the enthalpy production due to viscous effects, and Q denotes the volumetric heat input. The last term on the right hand side represents the total contribution of work by external body forces. External body forces b i and volumetric heat sources Q are normally not present or small in flames, and are therefore neglected. The heat flux vector is given by, q ρ N g s i 1 U i Y i j i λ T q R, (2.9)

25 16 Chemically reacting stagnation flow which consists of transport of energy by mass diffusion, conduction and radiation respectively. In section it was concluded that gas radiation is negligible in thin premixed flames. The reciprocal thermal diffusion effect, so-called Dufour effect, is not given because it can mostly be neglected in laminar premixed gaseous flames [135]. The specific velocity is defined as u i u U i, with U i the diffusion velocity of species i. The velocity of the gas mixture, or local bulk mass-averaged velocity, is defined as Because the summation of mass fractions u N g s i 1 Y i u i. (2.10) Ns g Y i 1, (2.11) i 1 it can be concluded that the mass-averaged diffusion velocity vanishes, N g s i 1 Y i U i 0. (2.12) Finally, conservation of chemical components is given by the transport equations in terms of mass fractions, ρy i ρu i Y t i ω i, (2.13) with ω i the chemical source term of species i, which is defined as the mass production rate of species i by chemical reactions. Chemical reactions conserve mass, hence Ns g ω i 0. (2.14) i 1 Then summation of Eq. (2.13) over all species will lead to the mass conservation equation, Eq. (2.5) Equations of State The set of differential equations is closed by the caloric equation of state and the thermal equation of state. The caloric equation of state determines the specific enthalpy and is given by j N g s i 1 Y i j i, j i T j ref i T T ref c pi T dt, (2.15)

26 2.2 Governing Equations 17 for a thermally perfect gas, with j ref i the formation enthalpy of species i at reference temperature T ref and c pi the specific heat capacity at constant pressure of species i, tabulated in polynomial form [67]. The overall heat capacity is c p N g s i 1 Y i c pi. (2.16) Since we are considering a mixture at relatively high temperature and atmospheric pressure, all species act as an ideal gas, and the thermal equation of state is given by the ideal-gas law, p M ρ (2.17) RT with R the universal gas constant and M the average molar mass, given by M N g s i 1 Y i M i 1, (2.18) where M i is the molar mass of species i. Because the velocities in laminar flames are much smaller than the speed of sound, the governing equations can be simplified using the low-mach number or Combustion Approximation [14] resulting in a constant pressure p p atm [101] in Eq. (2.17) Diffusion Models and Transport Coefficients In order to solve the set of equations, it is nescessary to know the species diffusion velocity U i, mixture average viscosity η and thermal conductivity λ. An extensive outline on multicomponent diffusion can be found in e.g. [10, 77, 35]. There are two ways to determine the diffusion velocities U i. The first, more accurate, model is to acquire U i from the multicomponent diffusion equation. If thermal diffusion (Soret effects [54]), body forces, and pressure induced diffusion are neglected, the diffusion equation can be written as a Stefan-Maxwell-equation [35], X i N g s j 1 X i X j D i j ( U j U i ), (2.19) with X i Y i M/M i the mole fraction of species i, and D i j the binary diffusion coefficient, which is independent of the mixture composition. The binary diffusion coefficients can be obtained from the transport library EGLIB [40]. However, to obtain U i during flame computations, inversion of a matrix is required, which is an elaborate task. The second, more simplified, method is to write the diffusion velocity as a Fick-like expression, U i Y i D im Y i (2.20)

27 18 Chemically reacting stagnation flow where D im is the mixture-averaged diffusion coefficient [53] which denotes the diffusion of species i in the mixture, and is obtained from D im 1 Y i. (2.21) Ns j g i X j/d i j The importance of thermal conduction with respect to species diffusion is given by the so-called Lewis numbers, λ Le i. (2.22) ρd im c p The conservation equations of enthalpy and chemical components, Eqns. (2.8) and (2.13) respectively, can be written in terms of Le i, and can be simplified significantly if Le i 1 for all species. However, in oxy-fuel flames, especially when hydrogen is involved, generally Le i 1. The mixture-averaged thermal conductivity λ is approximated by [90] λ 1 Ns g N g 1 s X 2 i λ i X i /λ i, (2.23) i 1 where λ i is the thermal conductivity of species i. This approximation has hardly any effect on the burning velocity [10]. The mixture-averaged dynamic, or shear viscosity is approximated by [137], η N g s i 1 i 1 X i η i Ns j g, (2.24) 1 X jφ i j where η i is the viscosity of species i, and Φ i j is given by. ( ) 1 Mi 1 ) ( ( ) 2 ηi 1 ( 2 Mj ) 1 ) 2 4 Φ i j 8 (1 1. (2.25) M j The values of η i and λ i are derived from polynomial fits once again [67]. With all transport coefficients and diffusion velocities known and substituted in the conservation and state equations, the Ns g +7 variables, u, ρ, T, j, p and Y i s can be determined using the Ns g 5 conservation equations, Eqns. (2.5), (2.6), (2.8), (2.13), and the two state equations, Eqns. (2.15), (2.17). The only remaining parameter to be known is the chemical source term ω i. In the next section we will discuss gas chemistry and an expression for ω i will be derived Gas Chemistry The combustion of a hydrocarbon is usually presented by a global reaction in molar form, C x H y O z νo 2 xco 2 y 2 H 2O (2.26) η j M i