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SP Technical Research Institute of Sweden

Mich

ael Förs

sth, Ken

S

nneth Mö

Fire Techn SP Report 20

öller

nology 011:75

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Absorption of heat radiation in liquid

droplets

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Abstract

Absorption of heat radiation in liquid droplets

The interaction between radiation from fires and single water droplets has been investigated in detail. A literature study was performed on available information of radiation spectra from different types of fires. Based on this, four reference spectra were proposed that cover most of the different types of radiation that can be expected from fires. These reference spectra were used to compare the effect of different droplets sizes and water additives later in the report.

Using Mie-theory it was found that increased atomization, down to a diameter limit of 1 – 10 m, gives a better volumetric absorption efficiency. Decreasing the diameter further does not lead to improved volumetric absorption since the Rayleigh (small droplet) limit is reached, where the volumetric absorption is independent of diameter. In fact there is a maximum in the volumetric absorption occurring for droplets of diameter 1 - 10 m. This maximum is typically on the order of 10% higher than the Rayleigh limit.

Different additives were investigated with respect to increased absorption in the droplets. It was found, however, that it is not trivial to find non-flammable and non-toxic additives that give a significantly improvement in absorption over that of water. Carbonated water was a potential candidate but the increased absorption was limited to a very weak band centered at 2300 cm-1. Since this coincides with the strong CO

2 emission band an effect

could be seen when carbonated water interacted with radiation from clean flames. The maximum increase in volumetric absorption was 4%, occurring for a droplet diameter of 10 m. Other additives gave better effects but they were either combustible (carbon nanopowder) and/or toxic to some degree.

Key words: absorption, scattering, drop, spray, drop size distribution, Mie theory, IR-radiation, fire

SP Sveriges Tekniska Forskningsinstitut

SP Technical Research Institute of Sweden SP Report 2011:75

ISBN 978-91-87017-07-0 ISSN 0284-5172

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Contents

Abstract 3

 

Contents 4

 

Nomenclature 5

 

Preface

7

 

Summary 8

 

1

 

Introduction 10

 

2

 

Thermodynamic boundaries of water sprays

12

 

2.1  Heating and vaporization of water 12 

2.2  Atomization 13 

2.3  Kinetic energy 14 

2.4  Energy comparisons 14 

3

 

Radiation spectra from fires

16

 

3.1  Radiation from hot surfaces: blackbody radiation 16 

3.2  Radiation from flames 17 

3.3  Selection of benchmark spectra 20 

3.3.1  Burning low density fiber board: bb700 20 

3.3.2  Hot smoke gas layer: bb1200 21 

3.3.3  Pool fires: bb1200e02Lor2300w85h13 21 

3.3.4  Clean flames from burning solid organic fuel:

Lor2300w75h25Lor3700w300h1 24 

3.3.5  Summary of reference spectra 25 

4

 

Absorption of radiation in droplets

27

 

4.1  Absorption of radiation in droplets: Mie theory 27 

4.2  Spectrally averaged absorption 32 

4.3  Water with additives 36 

4.3.1  Soluble additives 37 

4.3.2  Insoluble additive: Carbon nanopowder 39 

4.3.3  Absorption in water droplets with additives 42 

5

 

Conclusions 47

 

Appendix A: Transformation between M

and M

48

 

Appendix B: The Kramers Kronig relation

49

 

Appendix C: Measurement of volume fraction carbon

nanopowder 52

 

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Nomenclature

Abbreviation Quantity Unit Explanation/comment

A total area [m2]

a droplet surface area [m2]

c specific heat [JK-1kg-1]

c0 speed of light [ms-1] c0 = 2.99792458108 ms-1 (exact)

in vacuum

absorption cross [m2] section

volumetric absorption [m-1]

cross section

cp specific heat capacity [Jkg-1K-1] cp = 4.18·103 Jkg-1K-1 of water at constant

pressure

F radiant power [W]

I intensity [Wsr-1] Radiant power per unit solid

Angle

∆Hvap heat of vaporization [Jkg-1] ∆Hvap = 2.26·106 Jkg-1 of water at constant

pressure

h Planck’s constant [Js] h = 6.62610-34 Js

irradiance [Wm-2]

kB Boltzmann’s constant [JK-1] kB = 1.38110-23 JK-1

L radiance [Wm-2sr-1] Radiant power per projected area

per solid angle

m complex refractive [ ]

index

M exitance [Wm-2] Exiting radiant power per unit

area n real part of [ ] refractive index N number of droplets [ ] V total volume [m3] v droplet speed [ms-1] absorbed power [W] energy of heating [J] volumetric energy of [Jm-3] heating kinetic energy [J] volumetric kinetic [Jm-3] energy surface energy [J] volumetric surface [Jm-3] energy vaporization energy [J] volumetric [Jm-3] vaporization energy  emissivity [ ]

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ρ density of water [kgm-3] ρ = 9.98·102 kgm-3 at 293 K  wavelength [m]  imaginary part of [ ] refractive index  wavenumber [m-1]  Stefan-Boltzmann’s [Wm-2K-4] 5,6710-8 Wm-2K-4 constant

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Preface

This work was partly sponsored by Ångpanneföreningens Forskningsstiftelse with Ref. No. 10-115 which is gratefully acknowledged.

Acknowledgment is given to the staff at SP who has contributed to this project. Special thanks to Leena Andersson for determining the volume fraction of carbon nanopowder. Prof. Pascal Boulet at Laboratoire d’Energétique et de Mécanique Théorique &

Appliquée (LEMTA) at Université Henri Poincaré in Nancy, France, is gratefully acknowledged for providing measurement data of spectral radiance from fires. Dr. Michael Klassen, Combustion Science & Engineering, Inc., and Prof. Jay Gore, Purdue University, are gratefully acknowledged for providing additional information about their pool fire experiments.

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Summary

The interaction between radiation from fires and single droplets has been investigated in detail using Mie theory.

Firstly the energy that a water spray removes from the fire by evaporation and heating of the water is compared to the energy required for atomization and acceleration of the water. It is seen that, for all realistic droplet sizes, the energy added by reducing the diameter and accelerating the water is always negligible compared to the energy of evaporation and heating.

Secondly, a literature study was performed on available information concerning radiation spectra from different types of fires. Based on the results of this literature study, four reference spectra were proposed that cover most of the different types of radiation that can be expected from fires. These reference spectra are used to compare the effect of different droplets sizes and water additives later in the report. The reference spectra are

bb700 blackbody spectrum for T = 700 K, corresponding to the radiation from a solid burning surface.

bb1200 blackbody spectrum for T = 1200 K, corresponding to the radiation from a hot smoke gas layer.

sooty flame a mix of blackbody radiation for T = 1200 K and a Lorentzian profile centered at 2300 cm-1, which is the center for the strongest CO2 band. (This spectrum is also denoted

bb1200e02Lor2300w85p13, which is explained in the report.) clean flame a mix of two Lorentzian profiles centered at 2300 cm-1 (CO

2) and

at 3700 cm-1 (H

2O/CO2). (This spectrum is also denoted

Lor2300w75h25Lor3700w300h1.)

Using Mie-theory it was found that increased atomization, down to a diameter limit of 1 – 10 m, gives a better volumetric absorption efficiency. Decreasing the diameter further does not lead to improved volumetric absorption since the Rayleigh (small droplet) limit is reached, where the volumetric absorption is independent of diameter. In fact there is a maximum in volumetric absorption occurring for 1 - 10 m diameter. This maxima is typically on the order of 10% higher than the Rayleigh limit.

Different additives were investigated with respect to increased absorption in the droplets. It was found, however, that it is not trivial to find non-flammable and non-toxic additives that gives a significantly higher absorption than water. Carbonated water was a potential candidate but the increased absorption is limited to a weak band centered at 2300 cm-1.

Since this coincides with the strong CO2 emission band for the clean flame reference

spectrum an effect could be seen when carbonated water interacted with radiation from such flames. The maximum increase in volumetric absorption was 4%, occurring for droplet diameter of 10 m.

The possibilities for increased absorption in fire suppression sprays is interesting but more investigations are needed in order to identify better additives. One alternative could be to add non-flammable non-soluble nanoparticles that scatter the light inside the droplets, thereby increasing the distance the radiation travels inside the droplets. An increased concentration of CO2 in the droplets would be beneficial since radiation spectra

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from fires typically contain a large fraction of energy emitted from CO2. It would

therefore be of interest to add, for example, nanoparticles which contain large amounts of CO2.

Finally, it should be emphasized that this study was performed for single droplets. In order to quantify absorption effects in real fire scenarios it will be necessary to solve the radiative transfer equation in sprays and take into account the deformation of the radiation spectrum as the radiation passes through the spray.

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1

Introduction

An important feature of water sprays from fire suppression water mist systems is that the radiative heat transfer from the fire [1] to surrounding objects is reduced, thereby

reducing the fire spread [2-4]. Experiments have shown that as much as 70% of the heat radiation might be blocked due to this effect [5]. The reduction is due to absorption of radiation in the droplets or scattering of the radiation in different directions. It should be realized, however, that backscattered radiation will not necessarily reduce the fire since radiation from the burning object is then reflected back to the object, and the pyrolysis rate might actually increase. Absorption of radiation in the droplets is therefore the most interesting fire suppressing effect, not only because of radiation blocking but also because the heating and evaporation of the droplets is then promoted. Evaporation leads to a volume increase of a factor 1700 when the liquid water is transformed into gas. In enclosures this leads to a reduction in the partial pressure of oxygen, which inhibits the combustion process.

The absorptivity of water is relatively high for the spectral ranges where most of the energy from fire induced heat radiation is found. On the other hand the distance that the radiation actually travels through the droplets is relatively short [6]. It is therefore of interest to understand in detail how the droplets absorb radiation and how this process can be optimized.

The rationale of this study is twofold. Firstly the aim is to investigate which droplet sizes are most efficient in absorbing heat radiation from typical fire spectra. Secondly, to investigate which possibilities exist of enhancing the absorption by including additives in the water used to create the droplets.

The interaction between droplets and radiation has received considerable interest not only in the fire sciences but also in spray combustion technology. Lage and Rangel [7]

calculated the internal distribution of blackbody radiation absorption in water and decane droplets. The rationale for their study was to investigate different liquid heating models in single droplet vaporization [8], which is of great importance in spray combustion.

Harpole [9] studied the radial dependence of droplets on the absorption of black body radiation up to 1450 K. Dombrovsky and Sazhin [10] studied the spatially resolved absorption inside single droplets and developed a simplified analytic expression for the absorbed power. Dombrovsky [11] developed an analytical solution for optically thick polydispersed sprays. Godoy and DesJardin [12] determined the time evolution of droplet size distributions for radiation driven evaporation. The relation between scattering and absorption was investigated by Viskanta and Tseng [13] for droplet diameters between 10 – 500 m and for wavelengths 0.2 – 100 m. It was found that scattering dominates for small droplets and short wavelengths, while absorption becomes important for larger droplets and longer wavelengths. Dembele et al. [14] presented a radiative transfer model taking both the liquid and gaseous water phase into account. They also performed a sensitivity analysis on the parameters in their model.

Collin et al. [15, 16] modeled the spray dynamics and transmittance through realistic heterogeneous sprays. Absorption in the liquid water droplets as well as in the gaseous atmosphere were considered, and good agreement between simulations and experiments were found. The transmittance through water curtains was studied in references [17, 18]. Hostikka and McGrattan [19] developed a numerical model for radiation transport in polydispersed sprays and compared their results with experimental data. It was found that the model agreed with experiments provided droplet interaction could be ignored.

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Consalvi et al. [20-22] modeled the interaction between a compartment fire and a water mist. The interaction between the radiation and water droplets as well as combustion products were taken into account. It was found that the reduced radiation was not only due to absorption in the spray but also due to cooling of the flames, which resulted in lower emission of radiation. Another conclusion was that polydispersed sprays are more efficient than monodispersed sprays at reducing radiation. They also studied the error introduced by computing radiative transfer in sprays using spectrally averaged properties, the gray assumption, instead of spectrally resolved properties. It was found that the gray assumption gave reliable results as long as the sprays were optically thin.

Yang et al. [23] elaborated detailed information about absorption and angularly resolved scattering of radiation from water droplets in the range 10 – 500 m, for different wavelengths. These results were used as input to radiative transfer calculation in order to predict the penetration of thermal radiation into water mists.

In this report only the interaction between radiation and single droplets is considered. The effects of liquid temperature and gas phase absorption are ignored.

Section 2 gives a general overview of the thermodynamic properties of water sprays and the effect of droplet diameter. In Section 3 typical radiation spectra are discussed and the four reference spectra, to be used in the rest of the report, are described. Section 4 contains the core results of the report and discusses absorption as a function of droplet diameter and fire source spectrum. The effect of additives in the water is also

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2

Thermodynamic boundaries of water

sprays

In this study we will assume that the droplets in the spray are spherical. The two main reasons for this assumption are that volume considerations become very simple with spherical droplets and that the interaction of radiation with spherical droplets is theoretically manageable, albeit not particularly simple, using Mie theory [24]. The validity of this assumption can be questioned, for example, when drag forces on the droplets due to velocity differences as compared to the surrounding air, are important. The scope of this study is, however, to investigate the interaction between liquid sprays and radiation from a fire. For such applications the droplets can be considered spherical during most of their effective lifetime, that is the entire lifetime of the droplet minus the time of deceleration near the nozzle and the possible time of an collision with a solid object.

2.1

Heating and vaporization of water

For a water volume V, the required energy to heat the water from the injection temperature T0 to the boiling point Tboil (393°C at atmospheric pressure), the required energy is

where

cp isthe specific heat capacity of water at constant pressure, cp = 4.18·103 Jkg-1K

-1[25]. c

p is essentially independent of temperature in the relevant temperature range 293-393 K.

ρ is the density of water, ρ = 9.98·102 kgm-3 at 293 K [25]. ρ decreseas by 4% when

the temperature is increased to 393 K but this has no effect on the calculation above since the injected volume V increases accordingly.

When the water has reached Tboil, all energy absorbed contributes to the evaporation phase transition from liquid to vapor (gas). The energy required to evaporate a volume V at Tboil is given by

where

∆Hvap isthe heat of vaporization of water at constant pressure, ∆Hvap = 2.26·106 Jkg-1 [25].

Assuming the injection temperature T0 is 293 K we obtain the ratio

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This means that the 87% of the heat absorbed from the fire goes to vaporization and 13 % goes to heating of the liquid water.

The discussion above has assumed that the water is in its bulk form. For droplet sizes considered in this report, the specific heat capacity and the heat of vaporization do not deviate significantly from the bulk value, but this is not necessarily true for very small droplets (<0.01 m).

Once vaporized the water will continue to extract energy from the fire gases by heating of the vapor but this is outside the scope of this work, which only considers liquid water.

2.2

Atomization

When a liquid of volume V is atomized into a monodispersed spray of N droplets each droplet takes a volume given by

4

3 (1)

where r is the radius of the droplets.

The energy due to surface tension forces is higher for a droplet than for bulk liquid. The energy of a droplet is higher than the bulk liquid, due to the surface tension γ. The surface tension γ is 7.3·10-2 Nm-1 at 293 K [25]. For a spray atomized into N monosized droplets

the total area is

3

4 4

3

(2)

The surface energy required to atomize a volume V of bulk water into droplets of radius r is

3

(3)

Denoting this in terms of the energy per volume gives: 3

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Where γ is the surface tension. Equation (2) is singular at r = 0 and Eq. (4) might be singular, depending on the d-dependence of γ. However, the limit r = 0 is only reachable mathematically since a physical lower limit occurs when only single water molecules remain. In this report water clusters with a diameter less than 0.01 m are not considered. The size dependence of the surface tension for droplets with a diameter larger than 0.01 m, considered in this report, is relatively small [26-28] and therefore the surface tension will be assumed constant.

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2

If sp an

2

An Fi Fi 10 Th ad en ex sm fin dr

.3

K

f drag forces peed v is give nd the kinetic

.4

E

n energy bud igure 1. E cr re igure 1 show 0-2 m – 103 he rationale f dded to the fi nergies are ve xtracted from mall droplets nely atomize rop size. Suc

Kinetic e

are neglected en by c energy per

Energy c

dget for a mo Energies for e reating surfa espectively. ws that the kin

m are very for drawing F ire environm ery small com

m the fire env

are expected ed sprays giv h beneficial

energy

d the energy volume is th

comparis

onodispersed evaporating w ace area, acce

netic energie y small in com Figure 1 is th ment, as comp mpared to th vironment, no d due to incr ve any additio effects of sm required to 1 2 herefore 1 2

sons

d spray is giv water at 393 elerating to 10

es and the sur mparison to t hat the surfac pared to stati he evaporatio o negative ef reased surfac onal advanta mall droplets accelerate a ven in Figure K, heating w 0 ms-1, and a rface energie the evaporati ce and kineti ionary bulk w on and heatin ffects on the ce energy. Ra ages it is wor are increase volume V of e 1. ater from 293 accelerating to es in the diam ion and heati ic energies ar water. Since ng energies, w

firefighting p ather, this sho thwhile to de d heating an f water to the 3 K to 373 K to 1 ms-1, meter range ing energies. are actually these added which are properties of ows that if ecrease the nd evaporatio e K, . f on

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rates, and increased absorption of heat radiation. The effect of droplet size on absorption of heat radiation is the topic of this study.

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3

Radiation spectra from fires

The sources of heat radiation in fires are hot solid surfaces, hot smoke layers, and hot flames. In this section the spectral distribution of the radiation from fires is investigated. The purpose of this section is to define generic reference spectra that can be used to assess the effectiveness of water droplets to absorb radiation from different fire sources. In this report the spectral dependence is described using the wavenumber, , as the independent variable. In all figures the wavelength, , is also shown on an auxiliary upper x-axis. The relationship between  and  is simply:

 1 (5)

The unit used in this report for wavenumber  is [cm-1] and the unit for wavelength  is [m].

3.1

Radiation from hot surfaces: blackbody radiation

Radiation from a hot surface or from the soot particles in a hot smoke layer is

characterized by its blackbody exitance, M, which is expressed in Wm-2. This is expressed

by the Stefan-Boltzmann law that gives the total exitance for a blackbody source as:

(6) with unit Wm-2. The Stefan-Boltzmann’s constant,  is defined by

 2

15 (7)

where

h is Planck’s constant,

c0 is the speed of light in vacuum,

kB is Boltzmann’s constant.

The subscript “bb” refers to a perfect blackbody emitter. The spectrally resolved radiant exitance from a perfect blackbody emitter is given by

,

2

exp 1 (8)

where  is the wavenumber (inverse wavelength). The unit for Mbb, is Wm-2cm (power

divided by area divided by wavenumber, that is, divided by inverse wavelength). In this expression it is assumed that the dependence of the refraction index, n, on the

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air as wa Ex Fi ac Fi If by Fo em su wh le

3

Th ac tem pr fla r the refracti ssume n = 1 i avenumbers. xamples of th igure 2. It is ccordance wi igure 2 S f the irradianc y the exitanc or a real hot missivity sou urface receivi

here the subs ss than one.

.2

R

he soot in a s ccording to e mperature an roperties of th ame, or from

ive index onl in this study. . he spectral b clearly seen ith expressio pectral black ce comes fro e in expressi surface the e urce where the ing the radia

 script “” ind In general s

Radiatio

sooty flame w expression (9 nd an emissi he soot, and m hot flue gas

ly differs from . Expression

blackbody ex that the exita n (6). kbody exitanc om a perfect b ion (8). Real exitance is gi e subscript “s ation. The exi

,

dicates that t

source depends

n from f

will emit bla ). Sometime vity. The em the thicknes ses in the fire

m unity on th (6) is obtain xitance for di ance increas ce for differe blackbody em hot surfaces iven by the b source” refer itance from a , the expressio s on the wave

flames

ackbody radia es flames are missivity depe ss of the soot e plume, also he fourth dec ned by integr fferent temp es strongly w nt temperatu mitter the sp s are not perf blackbody ex rs to the heat a real surface on is for a rea enumber. ation, or at le characterize ends on the s t layer. Howe o contains m cimal. There ating equatio eratures are with tempera ures. ectral distrib fect blackbod xitance multip source and n e then becom (9) al surface wit east general h ed by a black soot concentr ever, the radi olecular band efore we will on (8) over a given in ature, in bution is give dies however plied by the not to the mes th emissivity heat radiatio kbody ration, iation from a nds. A all en r. y n a

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m m str wh 53 as ba sm su no Fo so m a n of fla CO bl cr Fi Sp th su sp molecular ban molecule is em rongest CO2

hile the most 300 cm-1 (1.9

s one band at ands also exi mall contribu uch as O2 and ot significant or a clean pre oot is negligib measured by H near stoichio f the blackbo ame tempera O2 and H2O lackbody at t reated,. This igure 3. R b re is pectral prope he spectrally r uch date from pectrally reso nd is a relativ mitted. Most bands are ce t important H 9 m) [29, 31 t 3700 cm-1 d ist, such as H utions to the t d N2 is very w

tly affect the emixed flam ble, since litt Hertzberg et ometric meth ody curve for ature. It can b

molecular ba the flame tem is due to the Radiation from ar pressure. eference [31] s included in erties of radia resolved emi m the literatur olved emitted vely narrow w of the radiat entered at 23 H2O bands ar 1]. The H2O due to limited H2O at 1600 c total radianc weak due to radiation. me the molecu

tle soot is pre al.[31] and i hane/air flam r 2225 K whi be seen that t ands, and tha mperature, m lack of soot m a near-stoi The optical d and therefor the figure.) ation from fi itted power p re has been t d power per u wavenumber tion is emitte 300 cm-1 (4.4 re at 3600 cm bands at 360 d spectral res cm-1 (6.3 m e [30]. Radia their lack of ular bands do resent. An ex s shown in F me, at 2 bar pr ich is the the the emission at the overall meaning that n t in the premi ichiometric (9 depth was 25 re only the bl

ires are often per unit area transformed unit area, in r region wher ed from CO2 m) and 37 m-1 (2.8 m), 00 cm-1 and 3 solution in th m) for exampl ation from ho f electric dipo ominate and xample of suc Figure 3. Thi ressure. Also eoretical adia from the fla l radiation is no, or very li ixed flame. 9.1% methan 5-30 cm [31]. lackbody rad n reported as per unit soli into spectral all directions re radiation f and water in 00 cm-1 (2.7 , 3800 cm-1 3800 cm-1 ar he measurem le, but these omo-nuclear ole moment [ blackbody ra ch a spectrum s shows the s o shown in th abatic constan ame is entirel much less th ittle, blackbo ne) methane/a (The figure is iation from t spectral radi id angle. In th exitance wh s. By assumi from a certai n a fire. The m) [29, 30 (2.5 m), an re often seen ments. Other are weak wi r molecules [32] and doe adiation from m was spectrum fro he figure is p nt pressure ly due to the han that of a ody radiation air flame at 2 is adapted fro that reference iance. This is this report all hich is the

ing that fires in 0] nd n th es m om part n is 2 om e s l

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emit radiation isotropically as a perfectly diffusive surface, that is in no preferred

direction, the spectral exitance is simply obtained by multiplying the spectral radiance by  [33]. Whether this assumption is correct or not is of no importance in this report since the focus of the study is on the spectral distribution of the emitted radiation, rather than on the absolute values of the radiation.

A more important issue is that spectral data is sometimes presented as a function of wavelength and sometimes as a function of wavenumber. In this report wavenumber is used in all figures and the wavenumber dependent spectral exitance, M, is presented.

When the wavelength dependent spectral exitance M is transformed into M the spectra

are reshaped. The transformation from M to M is explained in Appendix A. The

wavelengths are indicated at the top of the figures in this report. This is simply to help the reader who is more familiar with wavelengths than with wavenumbers. Note, however, that the total exitance [Wm-2] is obtained by integrating M

 over all wavenumbers, not

over all wavelengths.

Radiation spectra with rich spectral structures of molecular bands, with negligible contributions from blackbody radiation, are expected to be found mainly in the flames from premixed combustion. This combustion mode is seldom found in fire applications, the exception being explosions [31], and such spectra are therefore not considered further in this report.

When a solid fuel is burning the spectral characteristics of the radiation will be very sensitive to where in the fire the radiation is observed. If the flames above the fuel are observed there will be contributions from the blackbody radiation of the soot, if present, but not from the hot pyrolyzing fuel itself. If, on the other hand, the object that is on fire is observed there will also be contributions from the hot solid fuel, which acts as an almost perfect blackbody. This is illustrated in Figure 4 where data from Parent et al. [34] is presented. The solid graph shows the radiation from the flames and hot gases 10 cm above a 50 cm wide tray with burning wood and wine branches. Molecular bands are seen, especially the CO2 band at 2300 cm-1, but the contribution of blackbody radiation is

very weak. The dashed graph shows the radiation when the burning material itself is observed. Clearly the hot embers in the tray contribute significantly with blackbody radiation to the total heat radiation.

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Fi

3

Th ad sp Fo se sh

3.

M co th bu su its [3 ph di th ra 72 sc in igure 4. S

.3

S

he purpose o dditives, abso pectra which or this purpo electing these hown in Figu

.3.1

B

Measuring the onventional m he flame zone urning mater urface, i.e. ne s wires may a 5] used an a hosphorescen iagnostics, w he surface tem adiation is de 23K, is round cenario will b nvolved in a f pectral radia

Selection

of this project orb radiation will serve as se four diffe e specific spe ure 9.

Burning lo

e surface tem method is to e near the sur rial. It is there either in the g affect the he lternative me nt particles d which is non-i mperature of escribed by te ded off to 70 be referred to fire where ra

ance from bur

n of benc

t is to study h n from fires. I

s references i rent spectra ectra, are pre

ow densit

mperature of a

use small the rface are larg efore a chall gas nor insid at and air tra ethod, therm doped into the

intrusive, is u f burning low emperatures 00 K in this re o as “bb700” adiation from rning wood w

chmark s

how water d It is therefore in the compa will be used esented below

ty fiber bo

a burning ma ermocouples ge, and the te enge to posit de the materia ansport at the mographic ph e burning ma used to evalu w density fibe in the unit K report. The bl ” and is the re m molecular b

wool and win

spectra

droplets, and e necessary t arisons of dro . The spectra w. A summar

oard: bb7

aterial is not s. However, t emperature d tion the therm al. Furtherm e point of me

osphors. Thi aterial as tem uate the temp er board to 4 Kelvin, this te

lackbody spe eference spec bands are ign

e branches [3

water drople to select a nu oplet sizes an a, and the rat

ry of the fou

700

straightforw temperature decreases ins mocouple ex ore the therm easurement. O is method use mperature sen perature. The 50 C. Since emperature, 4 ectra corresp ctrum for a h nored. 34]. ets with umber of nd additives. tionale for ur spectra is ward. A gradients in side the xactly at the mocouple and Ossler et al. es tiny nsors. Optica ey measured e blackbody 450 + 273 = ponding to th hot surface . d al his

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3.3.2

Hot smoke gas layer: bb1200

The radiation to walls and floors from the smoke gas layer is an important heat transfer mechanism in enclosure fires. A very large number of temperature studies of such fires has been performed. In this report we select the results from an investigation of

appropriate design fires for train compartments [36]. A full scale test of a fire in a train compartment of a Swedish train, built in 1985-1986, was performed. The fire was initiated by igniting a seat with a 7 kW propane burner, see reference [37]. Two minutes after ignition, the temperature of the gas layer 10 cm below the ceiling flattened out at approximately 900C. This temperature, 900 + 273 = 1173, is rounded off to 1200 K. By assuming that the ceiling assumes the same temperature as the gas layer, and ignoring molecular bands, the spectra corresponding to this scenario will be referred to as “bb1200” and is the reference spectrum for a hot smoke gas layer, or maybe rather for a surface at 1200 K. Another interpretation for this reference spectrum is that it shows the radiation from large soot particles acting at black bodies at 1200 K.

3.3.3

Pool fires: bb1200e02Lor2300w85h13

A handful of spectrally resolved measurements of radiation from pool fires are available in the literature. The work by Suo-Anttila et al. [38] concerns the radiative feedback downwards to the fuel surface and is not considered here since the interest is in radiation from a fire to its surroundings, and not to the liquid fuel itself. The work by Raj [39] treats very large LNG (Liquified Natural Gas) pool fires, observed at relatively long distances from the fire. This means that some spectral parts of the radiation are heavily attenuated in the atmosphere and this work is not considered here. Instead the results by Hägglund and Persson [40] and by Klassen and Gore [41] are chosen as the basis for a reference spectrum for pool fires.

In reference [40] JP-4 pool fires of different sizes were studied. JP-4 is a jet fuel consisting of kerosene and gasoline. The radiation was measured at a level of 50 cm above the fuel surface. Different pool sizes, giving different flame thicknesses, were investigated. Figure 5 shows the radiation for two different flame thicknesses, 50 cm and 150 cm. These spectra are dominated by continuous blackbody spectra, from soot, overlapped with molecular bands at 2300 cm-1 (CO

2), 3700 cm-1 (CO2 and H2O), and at

5300 cm-1 (H

2O, barely seen as a bump on the blackbody curve). When the flame

thickness is increased, the total radiation and the relative importance of the blackbody radiation from soot, increase.

(22)

Fi Fi ty ar is th igure 5. S ob igure 6 show ype [41]. It is re similar for more import he pool was 3 pectral radia bserved 50 cm ws how the sp clear that, w r toluene and

tant for tolue 30 cm and th

ance from the m above the f pectral distrib while the stre d heptane poo ene, which is e observation e flames of JP fuel surface. bution of the ength of the f ol fires, the c s the most so n was made P-4 pool fires e radiant ener flame radiati contribution f ooty of the tw 30 cm above [40]. The rad

rgy can depe on in the mo from blackbo wo flames. Th e the fuel sur

diation was end on the fu olecular band ody radiation he diameter rface. el ds n of

(23)

Fi Ba pa bl cm T 23 13 bb fir an igure 6. S ased on the a articular [40, lackbody rad m-1. A sugges = 1200 K, em 300 cm-1 with 3 Wm-2cm. T b1200e02Lor re. The expre

nd is shown i

pectral radia available lite 41], it seem diation as the stion for such missivity so h a half widt The spectrum r2300w85p1 ession for thi

,

in Figure 7. M

ance from flam rature in gen ms reasonable main constit h a reference urce = 0.2, an th at half max m with these c 3, and is the is spectrum i Mbb,is given mes of tolue neral, and on e to create a s tuent with an e spectrum is nd to add a Lo ximum HWH constituents e reference sp is: n by expressi ne and hepta n the graphs i sooty pool fi n overlappin s to use a bla orentzian lin HM = 85 cm-1 will be refer pectrum for s ion (8).

ane pool fires n Figure 5 an re spectrum g strong CO2

ackbody radia e shape cent and peak val red to as sooty flames (10) [41]. nd Figure 6 i based on 2 peak at 230 ation source tered at 0 = lue of M0 = from a pool in 00 at l

(24)

Fi

3.

Bo ra fro ra (P Bu PP A de in di th do a s ba m ba m re Lo fro Th igure 7. T b

.3.4

C

L

oulet et al. h adiation from om fires in w adiance from, Polyoxymeth uckius and T P (Polypropy s was shown epends consi n reference [3 irected towar he burning em ominated by spectrum wit and with a Lo maximum HW and at with a maximum HW eference spec or2300w75h om a modera he spectrum The reference b1200e02Lor

Clean flam

Lor2300w

ave performe m wine branch wood cribs (s , and transmi hylene), and P Tien [30]. Ve ylene) in flam n in Figure 4 derably on w 34] much mo rds the burnin mbers. Since blackbody ra th little black orentzian lin WHM = 75 cm Lorentzian l WHM = 300 cm ctrum. The s h25Lor3700w

ate fire in sol is described spectrum co r2300w85h13

mes from

w75h25Lo

ed a number hes, wood w spruce) were ittance throu PMMA (Poly ervisch and C ming and smo the amount a where in the f ore blackbody ng embers th the referenc adiation it is kbody radiat ne shape cent 1 and M0 = 2 line shape ce m-1 and M0 = pectrum with w300h1 and lid organic fu by the formu orresponding 3.

burning s

r3700w30

r of studies o wool, and oak performed b ugh, flames fr y(methyl me Coppalle [45] oldering com and distribut fire the obse y radiation is han when it w ce spectrum f appropriate tion. Therefo tered at 0 = 25 Wm-2cm. entered at 0 = 1 Wm-2cm. h these const is the referen fuel. ula to a sooty fla

solid orga

00h1

n the spectra k shrubs [34, by Hägglund from polystyr ethacrylate)) ] measured th mbustion. tion of radiat rvation is ma s observed w was only dire for a pool fire to select the ore this spectr

2300 cm-1 w Further, a w = 3700 cm-1 No blackbo tituents will nce spectrum ame:

anic fuel:

al distribution 42, 43]. Mea d and Persson rene, POM were perform he spectral ra

tion from fire ade. In the m when the spec ected into the e, see Figure

last referenc rum is domin with a half wid weaker mixed with a half w dy part is inc be referred t m for non-soo n of the asurements n [44]. Spect med by radiance from es in solid fu measurements ctrometer wa e flames abo e 7, is ce spectrum nated by a C dth at half d H2O/CO2 width at half cluded in thi to as oty flames ral m uel s as ove as CO2 f s

(25)

an di is th in co Fi

3.

Th fa ga of m tw sp cle su di tw is nd is shown i istances betw the onset of he radiation w n so much abs onsidered mo igure 8. T L

.3.5

S

he spectral d actors as fuel ases). The ref f fire, but are main feature o wo blackbody pectrum whic ean flame sp ummarized in isplayed wav wo blackbody expected fro CO2 b in Figure 8. I ween the fire f a fire in a re will pass thro sorption in th olecular band The reference Lor2300w75h

Summary

distribution o , fire size, an ference spec e rather simpl of the four sp y spectra at r ch contain bo pectrum whic n Figure 9.Th venumber ran y spectra bb7 om the Stefan band It should be n and the abso esidential enc ough water an he atmosphe ds. spectrum co 25Lor3700w3

of refere

f the heat rad nd observatio tra chosen ab ly four spect pectra is that relatively col oth blackbod ch is dominat he spectra ar nge, here 0-1 700 and bb12 n-Boltzmann noticed that orbing surfac closure. For nd CO2 in th

ere that dips a

orresponding 300h1.

ence spect

diation varie on point (glo bove are not tra that are no

they cover a ld and hot co dy radiation f ated by the C re normalized 10000 cm-1, i 200 are simil n law, see ex mixed H2O this spectrum ce. An examp radiative tran he atmospher are observed to a clean fla

tra

s considerab owing embers meant to ful ot unrealistic a wide range onditions resp

from soot and O2 band at 2 d such that th s 1 Wm-2cm lar in amplitu xpression (1). O/CO2 band (( m is valid onl ple of such a nsfer over lo e. This may , instead of p ame: bly depending s, flames, or lly characteri c for each fir of spectral d pectively, a p d a CO2 band 300 cm-1. Th he total exita . This explai ude, in contra . (11)

nly for short a configuratio ong distances

in fact result peaks, for the

g on such hot flue rize each type re type. The distributions: pool fire d, and a woo he spectra are ance in the

ins why the rast from wha

on s t e e od e at

(26)
(27)

4

Absorption of radiation in droplets

4.1

Absorption of radiation in droplets: Mie theory

In order to calculate the absorption in droplets it is necessary to use the solutions to Maxwell’s equations developed by Mie [46]. The reason why it is not correct to simply study the liquid bulk properties are many. For example, the reflection and transmission at the droplet surface depends on the angle between the radiation and the droplet’s surface, and on the wavenumber dependent index of refraction. Furthermore complex

interference effects occur inside and outside the droplet.

The formalism used in this study is based on the work of Bohren and Huffman [24], with the main exceptions being that the droplet size in this report is characterized by the diameter d instead of the radius and that the spectral dependence is described by the wavenumber  instead of the wavelength .

The assumptions made are that the droplets are spherical, that the refractive index of air is unity, and that the radiation is hitting the droplet as plane unpolarized waves.

The absorption cross-section Cabs is defined as the absorbed power divided by the irradiance Ii:

1

2  2 1 Re | | | | (12)

Where the scattering coefficients an and bn are expressed by [24, 47]:

(13)

(14)

where m is the complex refractive index and x is the size parameter, defined in expressions (15) and (16), respectively.

The refractive index consists of a real and an imaginary part:

(15)

where the real part n is a measure of the decrease of wavelength in water and  is a measure of the attenuation of the irradiation as the radiation penetrates into water.

(28)

Fo pl Fi Th wh Th [4 Th Th [4 fu In th in 1 h or pure water lotted in Figu igure 10. R re he size param here d is the he functions j 49], respectiv he prime ind he numerical 47, 50, 51] an unctions, and n general it is heir larger cro nteresting to s hn(1)(x) is also r n and  we ure 10. Real (n) and im eference [48] meter x is def droplet diam jn(x), and hn vely1. dicates differe l computatio nd a discussio d other numer s clear that fo oss-sectional study the abs

sometimes ca re tabulated maginary () . fined by:  meter and  i (1)(x) are sph entiation wit ns are perfor on about the rical issues, c or single drop l area. From sorbed power alled a spheric by Hale and ) part of the r  s the wavenu herical Besse th respect to rmed using t e truncation c can be found plets larger d a spray effic r per volume

cal Hankel fun

d Querry [48] refractive ind umber, see ex el functions o the argumen he Matlab co criteria for ev d in reference droplets abso ciency perspe e of water. T nction [24]. ] and their va

dex for pure w

(16) xpression (5) of the first an nt within the p ode develope valuating the es [47, 50, 52 orb more radi

ective it is th herefore the alues are water. From ). nd third kind parentheses. ed by Mätzle e Bessel 2-54]. iation due to herefore quantity d er o

(29)

wi vo Ca re Fo 10 dr ex It ab Fi Th ra lo vi be th ra rip sin 2 I div sim

ill be the abs olumetric abs alculations w esolution of 0 or each dropl 0000 cm-1 wi roplet diamet xpected highe is also seen bsorptivity. igure 11. he ripple and adiation cann garithmic sc isible and it h e interpreted hrough the dr adiation pene pple and inte nce the exact In the Matlab vided by the g mply been mu sorption para sorption cros were perform 0.01 m for let diameter ith a resolutio ters for diffe est for waven that the diam

as a funct d interference not be observ cale, see Figu has a strong r as interferen roplet. Accor etrates throug erference stru t values of code by Mätz geometrical cr ultiplied by 3/( ameter emplo ss-section is

med for drople 10-2–1 m, 0 calculations on of 10 cm -rent wavenu numbers whe meter depend tion of drople e structure th ved in Figure ure 12. Now ripple and in nce between rdingly, for s gh the drople uctures in Fig is sensiti zler [47] the o ross section of (2d). oyed in the re defined as2 6 et diameters 0.1 m for 1– were perform -1. In Figure umbers of the ere the bulk dence is stron

et diameter fo hat is typical e 11 but can b the weak abs nterference st

the external strong absorp ets and the in gure 12 shou ively depend output is Cabs/( f the droplet. I emainder of in the range –102 m, and

med for wav 11 is sh e radiation. T absorptivity ngest for wav

or fixed wave in Mie-scatt be seen if the sorption for tructure. Thi radiation fie ption such as nterference st uld only be c dent on diam (r2), that is th In order to ob this report. T (17) 10-2–103 m d 10 m for venumbers be hown as a fun The absorptio , see Figure venumbers w enumbers. tering with m e -axis is 10000 cm-1 r s behavior ca eld and the ce for 3330 cm tructure is sm onsidered as eter and wav

he absorption tain this This m with a 102–103 m etween 400-nction of on is as 10, is highes with high bul

monochromat s shown on a radiation is an physically entral beam m-1 little mall [24]. Th s qualitative venumber. Th cross section output has . st. k tic a y e he

(30)

in un Fi If cle ab ex (1 wh vo wh ca th nterference an nderlying dro igure 12. f the diameter early for sma bsorption effi xpression for 2) to: here Im deno olumetric abs hich is indep alculations in hat must be sa nd ripple stru oplet diamete as a funct -axis. r axis is show all diameters ficiency appr r the absorpti Im

otes the imag sorption effic pendent of di n the asympto atisfied in or ucture in the er resolution tion of drople wn on a loga s, see Figure oaches asym ion cross-sec 1 2 ginary part o ciency becom 6 iameter. This otic behavior rder for expre

graphs is the n. et diameter fo arithmic scale 13. Firstly, f mptotic value

ction Cabs can

Im of the express mes Im 1 2 s size indepe r for small di essions (18) erefore stron or fixed wave e two import for small dia s. For small n be simplifie 1 2 sion within th 1 2 endence is als iameters in F and (19) to b ngly dependen enumbers, wi tant features ameters the v droplet diam ed [24] from (18) he parenthes (19) so observed f Figure 13. Th be valid is th ent on the ith logarithm appear more volumetric meters the m expression sis. The

from the Mie he condition hat

mic

e

(31)

wh co 1. wh in Fi Se in sm di fu re eq do hich will be omplex refrac 371 + i0.272 6 ∙ 3 hich is in per n Figure 13. igure 13. econdly, and n for d  mall diameter iameter limit urther to incre elatively sma quipment. In own to a limi 4 3 satisfied for ctive index f 2. Evaluating 3330 ∙ Im 1 1 6 ∙ 33 6 ∙ 33 rfect agreem as a funct -axis. d very interes  1 m. This r Rayleigh li t below whic eased volum ll diameter g most circum it of 1 – 10  Im 1 2 sufficiently for 3330 cm-1 g expression 1.371 0.2 1.371 0.2 330 ∙ Im 0.2 330 ∙ 0.1488 ment with the

tion of drople

sting for the d maximum is imit. The exi

h increased a metric absorpt

given the exi mstances the c m, gives a b 1 2 ≪ 1 small drople 1 (3 m) is g (19) gives 72 2 1.3 72 2 1.3 2409 0.14 8 9300 cm asymptotic v et diameter fo design of wa s typically ar istence of the atomization, tion by the li isting atomiz conclusion i better volume et diameters. given by Hale 371 ∙ 0.272 371 ∙ 0.272 488 m-1 0.93 μ value for sm or fixed wave

ater mist syst round 10% h ese maxima m or evaporati iquid droplet zation mecha s therefore th etric absorpti (20) As an examp e and Querry 1 2 m-1 (21) all diameters enumbers, wi tems, there is higher than means that th ion, do not co s. However, anisms in fire hat increased ion efficienc mple the y [48] as m = s for 3330 cm ith logarithm s a maximum in the here is a low ontribute 1 m is a e protection d atomization cy. = m-1 mic m er n,

(32)

These results further strengthen the conclusions by Fuss et al. [55] that decreasing the diameter to less than 10 m does not lead to an improved suppression capacity of premixed methane/air flames. Their conclusions were not based on absorption but on evaporation considerations and so two different types of analyses points towards a lower diameter droplet limit for fire suppression sprays.

For large diameters the droplets become much larger than the wavelength of the radiation. This means that the geometrical optics limit is approached. For weak absorption, which is the case for example for water at 10000 cm-1, the volumetric absorption becomes [56]:

4

1 (22)

As a numerical example, if =2.89·10-6 and n=1.327 for water at 10000 cm-1 according

to Hale and Querry [48]. The volumetric absorption becomes 4 ∙ 2.89 ∙ 10 ∙ 10000

1.327 1.327 1.327 1

0.46 cm-1 4.6 ∙ 10 μm-1

(23)

in good agreement with Figure 12. At wavenumbers with higher extinction coefficient expression (22) is no longer valid since the absorption becomes concentrated to the front surface of the droplet. The geometrical optics limit is therefore of little use for fire purposes since very small amounts of the heat radiation is found in the wavenumber ranges where the extinction coefficient of liquid water is very low.

4.2

Spectrally averaged absorption

The volumetric absorption efficiency in Figure 11 is given for different fixed wavenumbers, or in other words for monochromatic radiation. As was discussed in Section 3 the radiation from blackbodies and fires are continuous spectra of radiation with exitance as a continuous function of wavenumber. The total exitance M is the total

emitted power per unit area of the hot surface/flame and is given by:

M (24)

The effective volumetric absorption efficiency for a given spectra M is expressed as the

weighted average of as a function of wavenumber with the exitance M as weight

function.

,eff (25)

In this report the spectral averaging has been performed over the wavenumber range 400 – 10000 cm-1 (1 – 25 m). This part of the spectrum contains the major part of the total

energy for the temperatures of interest for fire considerations. The missing part is

quantified by integrating expression (8) between 400 – 10000 cm-1 and 10 – 100000 cm-1

(0.1 – 1000 m), and calculating the ratio between the integrals. The latter wavenumber range covers virtually all emitted energy at the temperatures considered. The result is

(33)

sh 40 Fi in hown in Figu 00 – 10000 c igure 14. F 1 , for di n Figure 15. ure 14 and it cm-1. Fraction of all 0000 cm-1, wh ifferent black is seen that a l emitted blac hich is the wa kbody tempe almost all en ckbody radia avelength int eratures with nergy is cover ation that is e erval conside h M given by red by averag mitted in the ered in this re y expression aging betwee e interval 400 eport. (8) are given n n

(34)

Fi It im ar d= dr vo In Th to Fi m th M av Th bl Fi fo dr (b th th ex Th sp m igure 15. d is observed mproved volu re essentially =1 m in tem roplets are al olumetric abs n general the he explanatio wards highe igure 10. Ano maximum in v his occurs is a Mie theory, th veraging. The he position o lackbody tem igure 16 show our reference roplets the re bb1200e02Lo he clean flam hat there is a m xtinction part he difference pectra decrea more or less th , as a fu droplet diame again that de umetric absor y identical) th mperature ran lmost identic sorption is in volumetric a on for this is r wavenumb other interes volumetric ab around 1000 he wavenumb e maximum of the maxim mperature in f ws the volum spectra in S esults are sim

or2300w85h me spectrum (

mismatch be ts of the liqu e in volumetr ases with incr he same as fo unction of bla eters. ecreasing the rption. On th he volumetric nge of interes cal is that the

ndependent o absorption de that for high bers, where th ting feature o bsorption wit K. The mec ber dependen cannot simp mum is somew fire scenario metric absorp ection 3.3.5 milar for bb70 13). By cont (Lor2300w75 etween the C uid water. Th ric absorptio reasing dropl or bb1200 an ackbody temp e droplet diam he contrary, f c absorption st. The reaso e Rayleigh lim of diameter, s ecreases with her temperatu he extinction of Figure 15 th respect to chanism behi nt complex re ly be explain what lucky si os. ption as a fun as weight fu 00, bb1200 a trast the volu 5h25Lor3700 CO2 emission his is seen by on between th let diameter nd the sooty perature of th meter below for d=0.01  is of the ord on why the re mit has been see expressio h increasing ures the blac n coefficient is that for sm temperature nd this maxi efractive ind ned by Wien ince 1000 K nction of drop unction M in

and the sooty umetric abso 0w300h1). T n peak at 230 comparing F he clean flam and for d30 flame spectru he radiationfo 10 m does m and d=0.1 der of 10% lo esults for the reached, wh on (19). blackbody te ckbody spectr for water is l mall droplets e. The temper mum is com ex of water, ’s displacem is a highly r plet diameter n expression y flame spect rption is muc The explanati 0 cm-1 and th Figure 8 and me spectrum a 0 m the abs um. for different not lead to 1 (these resul ower than for e smallest here the emperature. trum is shifte low, see s there is a rature where mplex involvi and spectral ment law [29] relevant er using the (25). For sm trum

uch lower for ion for this is he high d Figure 10.

and the othe sorption is lts r ed e ing l ]. mall r s r

(35)

Fi Th th bl an ra wa igure 16. F he volumetri hese large dro

lackbody rad nd the sooty f adiation is fou ater is low. , as a fu Figure 9. The ic absorption oplets it is se diation at 120 flame spectru und at high w nction of dro diameters ar n for large dro een that the a 00 K. The rea um (bb1200e wavenumber oplet diamete re shown on a oplets, 100-1 absorption is

ason for this e02Lor2300w rs, see Figure

r for the diffe a logarithmic 1000 m, is s lowest for th is that for th w85h13), a r e 9, where th erent referen scale. shown in Fig he two spectr hese two spec relatively larg e extinction nce spectra in gure 17. For ra with ctra, bb1200 rge part of th coefficient f n e for

(36)

Fi

4

On be m ad th hi wa NI th Th be W W Th igure 17. re

.3

W

ne of the rati e enhanced u measured usin dditive, was p he spectra [57 ighly infrared avenumber i IR (that is hi he radiant ene he spatial dep e expressed b Where k is the Where  is the he wavenum , as a fu eference spec

Water w

ionale for thi using additive ng a Nicolet positioned on 7]. This is a v d absorbing l interval 400 – igher wavenu ergy from fir

pendence of by [58]: e amplitude o e wavenumbe mber, , can m nction of dro ctra in Figure

ith addit

is study was es in the wat 6700 spectro n a diamond very fast and liquids such – 4000 cm-1 umbers) wer res is found i f an electrom exp of the wavev 2 2 er in the med mathematical oplet diamete e 9. The diam

tives

to determine ter. Absorban ometer. A dr micro-ATR d simple meth as water. Me (2.5 – 25 m re deemed ne in this region magnetic plan vector 2  dium. lly be expres r, for large d meters are sho

e whether the nce of water roplet of the w R (attenuated hod to condu easurements m). No measu ecessary sinc n, see Figure e wave prop ssed as droplets, for th own on a loga e radiation ab with additiv water, or wa total reflecti uct measurem were perform urements in t e only a sma 9. agating in di (26) (27) the different arithmic scale bsorption ca ves was ater with ion) to obtain ments on med in the the visible or all fraction o irection x can e. n n r f n

(37)

 

(28)

where m is the complex refractive index

(29) where

n is the real part of the refractive index, often simply called the index of refraction, and

is the extinction coefficient Expressions (26) - (29) gives

exp 2 exp 2

exp 2 exp 2 (30)

The energy flux I is proportional [58] to |E|2 and therefore

exp 4

(31) The absorbance A is defined as

log10 (32)

and therefore

log10 exp 4 4 log10 e

(33) Expression (33) shows that the absorpance A not only depends on the extinction coefficient but also on the wavenumber and propagation length x. However, the propagation length is proportional to the penetration [59] depth of the attenuated

evanescent field into the liquid. This penetration depth is proportional to the wavelength [59], that is inversely proportional to the wavenumber. Therefore the wavenumber and the propagation length x cancel each other out in expression (33) and we obtain, for these measurements:

(34)

4.3.1

Soluble additives

Figure 18 shows as an example the difference in absorbance between water and a mixture of water with 5.9 % (per weight) of Na2CO3 (sodium carbonate).

(38)

Fi A Th Fi co sig m co th Th ar en KH Na so as gi an an It Th em Fi in em 10 igure 18. M w s is observed his was also igure 18 and oefficient  d gnificant diff modify the -s omparison be he change in r he additives re expected to nvironmental H2PO4 (pota a2CO3 (sodiu oluble salt wh s ammonium ives of ammo nd applicatio nd animals. is clear that he only diffe mission band igure 19. It w ncrease in abs mission from 000 - 1500 cm Measured abs with 5.9% (by d in Figure 1 found for the

expression ( due to the add fference betw spectrum dev etween the H radiation abs were selecte o absorb in t l consideratio assium dihyd um carbonate hich is harmf bicarbonate onia upon he ns for fire su carbonated w erence is a ve ds centered at will, however sorption, esp m hot CO2 gas m-1 and 2500 sorbance usin y weight) Na2C 8, significan e other solub (34) is straigh ditive. The p ween pure tap veloped in H Hale and Que sorption of th ed based on c he relevant w ons. Unfortu rogen phosp e, also know ful to the eye

, or hartshorn eating. All th uppression is

water differs ery weak ban t 2300 cm-1 i r, be seen bel pecially for th s. The other 0-3000 cm-1. ng the ATR-te CO3. nt differences ble additives htforward to parts of the  p water and t Hale and Que erry spectrum he droplets w criteria such wavenumber unately the la phate) is a no wn as washing es. NH4HCO rn) is a non-f hese additives s therefore on s very little a nd at 2300 cm in Figure 3 to low that this he clean flam additives sho echnique for s only occur investigated o calculate th -spectrum w

tap water wit rry [48]. Fig m and the spe with additive as expected r range), solu ast criteria is n flammable g soda) is a n O3 (ammonium flammable w s are more or nly possible i s compared t m-1 (compare o Figure 6) w s slight increa me spectrum ows increase tap water an between 100 d. Using the r e change in e where there w th additives w ure 19 show ectrum used f s. absorption (e ubility in wat typically dif e water solub non flammab m bicarbonat ater soluble r less harmfu in spaces voi to non-carbo e with the stro which is bare ase in absorp containing m ed absorption nd tap water 00 – 3000 cm result from extinction was a were used to ws the for assessing e.g. carbonat ter, cost, and fficult to mee ble salt. ble water ate, also know

salt which ul to the heal id of humans onated water. rong CO2 ely visible in ptivity gives mostly n in the range m-1. g tes d et. wn lth s . an e

(39)

In sp th Fi

4.

Th so ve co Ho liq fie pr Th Al of ne pa na tra wa n order to per pectrum. This his analysis ar igure 19. E

.3.2

I

he changes in oluble additiv ery strong ab ombustible an owever, app quid, such as eld of applic roperties. he carbon na ldrich. Meas f the water/po ear the diamo art of the mix anopowder p ansparent to as measured rform the Mi s was done u re described Extinction coe

nsoluble

n extinction ves presented bsorber, was nd should th lications whe s radiation ab ation if the m anopowder, w surements us owder mixtu ond crystal, a xture. Instead per weight) an infrared radi d in the spectr ie-calculation using the Kra

in Appendix efficient  for

additive:

coefficient w d in Section 4 also investig erefore not b ere the flame bsorbing spra mixture of wa

with particle ing the ATR ure. Therefor and did not p d, the carbon nd pressed in iation in the rometer and ns it is also n amers-Kronig x B. r water with a

Carbon n

were centered 4.3.1. Theref gated. Carbon be used in dir es do not nec ay curtains fo

ater and carb

size < 0.05  R technique w re the evanes penetrate to t n nanopowde nto a 10 mm investigated  was calcul necessary to c g relations [4 additives as c

nanopowd

d to a few na fore carbon n n has the obv rect fire supp cessarily com or example, c bon nanopow

m, was purc were not poss cent field on the powder w er was mixed long pellet. wavenumbe lated from ex calculate the 48, 60, 61]. T compared to p

der

arrow spectra nanopowder, vious drawba pression of fl me in contact could be an i wder shows g chased from sible due to s nly penetrated which floated d in KBr (1% KBr is relati er range. The xpression (33 e modified n-The details o pure water. al bands for t , which is a ack that it is flames. t with the interesting good absorbin Sigma segmentation d the water d in the uppe % carbon ively e absorbance 3). -f the ng n r

(40)

Fo ca Th ba m be ca re wi Fi Th ca In us sp or the carbon alculated but his is a pragm ased on a Ray medium. Effec een neglected arbon nanopo easonably fitt ith  express igure 20. E ex he total extin alculated as a nstead, an eff sed approxim pherical the a n nanoparticl rather the ex matic hybrid yleigh absorp cts of the dif d. Figure 20 owder. As ca ted, at least i sed in [cm-1]. Experimentall xpression (35 nction coeffic a mass avera fective mediu mations is the average diele 1 les it is not th xtinction coe approach wh ption of sma fference betw shows the re an be seen in n the relevan 49 ∙ . ly determined 5).

cient for carb ge between t um approxim e Maxwell G ectric constan 1 3 1 he extinction efficient of a here an effec all spheres co ween the refra esulting extin n the figure th nt wavenumb . d extinction c bon nanopow the extinction mation can be Garnett [24, 6 nt, mix, is giv 2 2 n coefficient medium con ctive extincti onsidered to action index nction coeffic he experimen ber range, by coefficient  a wder in water n coefficient e used. One o 2-64] theory ven by of the soot th ntaining the n ion coefficien constitute a h for KBr and cient, transla ntal results ca y the expressi (35) and a curve f r cannot simp ts of water an of the most c y. If the carbo (36) hat is nanoparticles nt is calculat homogeneou d water have ated to 100% an be ion: fit according ply be nd carbon [2 commonly on particles a s. ted us % to 4]. are

(41)

wh fra va stu fro sa Th Th wh Ha wh Fi W Kr here f is the v action f was alidity of effe udy, where t om fires is in atisfactory. he dielectric he extinction here Im deno ale and Quer hich is a reas

igure 21. E n

When the mix ramers-Kron volume fract found to be ective mediu the qualitativ nvestigated, t constant  is n coefficient

otes the imag rry [48] whil sonable valu Extinction coe anopowder in spectrum wa nig relations, tion of the ca 7.5% for a w um approxim ve effect of ca the Maxwell s given by

for the mixtu Im ginary part an le carbon is ca ue for carbon efficient for w n water. as determine see Append arbon nanopa weight concen mations is sub arbon nanop l Garnett app ure is therefo nd mix is giv alculated fro [24]. Figure

water and for

ed the n-spec dix B. articles in the ntration of 5 bject to discu powder on the proximation i ore obtained ven by expres m expression e 21 shows th r a mixture of ctrum was ca e mixture. Th .9%, see App ussions [65] b e absorption is considered (37) as (38) ssion (36). w n (35). ncarbon he resulting  f 5.9% (by we lculated usin he volume pendix C. Th but for this

of radiation d to be water is given n is set to 1.7 -spectrum. eight) carbon ng the he by 7, n

(42)

4.

Fi an Fi Fo ab ad se co so na th

.3.3

A

igure 22 to F nd for the dif

igure 22. re 3 or all referen bsorption is s dditives. This ee Figure 19. oefficient. Th oluble additiv anopowder a herefore it is d

Absorptio

Figure 25 sho fferent refere , for diff eference spec .3.1. The diam nce spectra, w strongest for s correlates d The effect o he effect of c ve and pure w nd Na2CO3 a difficult to d

on in wate

ow the resulti ence spectra. ferent additiv ctrum bb700, meters are sh with the exce NH4HCO4 a directly with of CO2 is ver carbon nanop water. It shou almost coinc distinguish th

er droplet

ing volumetr ves as a funct , correspondi hown on a log eption of that and weakest the differenc ry weak due t powder is int uld be observ ide for the bb hem in Figure

ts with ad

ric absorption tion of drople ing to a hot b garithmic sca t for the clean

for KH2PO4

ces in increa to the very ti termediate be ved that the c b1200 and th e 23 and Figu

dditives

n for the diff

et diameter fo urning surfa le. n flame, the among the s ased extinctio iny increase etween the m curves for ca he sooty flam ure 24. ferent additiv or the ace, see Sectio

increased solid soluble on coefficien in extinction most efficient arbon mes spectra, ves on nt, n t

(43)

Fi Fi igure 23. re S igure 24. re fr sc , for diff eference spec ection 3.3.2. T , for diff eference spec rom a sooty f cale. ferent additiv ctrum bb1200 The diameter ferent additiv ctrum bb1200 flame, see Sec

ves as a funct 0, correspond rs are shown ves as a funct 0e002Lor230 ction 3.3.3. Th tion of drople ding to a hot on a logarith tion of drople 0w85h13, cor he diameters et diameter fo sooty smoke hmic scale. et diameter fo rresponding t are shown on or the gas layer, see

or the to radiation n a logarithm

e

References

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