<<

RADIATIVE CHARACTERISTICS OF A THIN SOLID

AT DISCRETE LEVELS OF :

ANGULAR, SPECTRAL, AND THERMAL DEPENDENCIES

by

RICHARD DALE PETTEGREW

Submitted in partial fulfillment of the requirements

For the Degree of Doctor of Philosophy

Thesis Advisors: Professor James S. T’ien (CWRU)

Dr. Kenneth Street (NASA GRC)

Department of Mechanical and Aerospace Engineering

CASE WESTERN RESERVE UNIVERSITY

January, 2006 CASE WESTERN RESERVE UNIVERSITY

SCHOOL OF GRADUATE STUDIES

We hereby approve the dissertation of

______

candidate for the Ph.D. degree *.

(signed)______(chair of the committee)

______

______

______

______

______

(date) ______

*We also certify that written approval has been obtained for any proprietary material contained therein. Copyright 2005 by Richard Dale Pettegrew All rights reserved

i Dedication

This work is dedicated to the loving memory of my mom and dad, Carroll and Lowell

Pettegrew. They taught me to dream big, take risks when necessary, and have the kind of work ethic needed to finish a project like this. Even more importantly, they believed in me when no one else did. While they are no longer here to see the completion of this work, I believe they know, and are proud.

Mom and Dad: I love you both, and thank you for everything!

i Table of Contents

Dedication ...... i List of Tables ...... iv List of Figures...... v Acknowledgements ...... vii Abstract...... viii 1.0 Introduction...... 1 1.1 Radiative Heat Transfer in Problems...... 2 1.2 Gas-Phase Radiation ...... 4 1.3 Surface Radiation...... 6 1.3.1 Reasons for Spectral Dependence ...... 7 1.3.2 Temperature Dependence & Thermal Effects...... 8 1.3.3 Angular Dependence...... 10 1.4 Radiative Interaction between Gas and Solid...... 10 1.5 Previous Knowledge of Optical Properties ...... 11 1.6 Objectives of This Study...... 13 2.0 Experimental Approach & Overview ...... 16 2.1 Premise and Assumptions...... 16 2.2 Data Acquisition and Determination of Spectral Properties...... 18 2.3 Determination of Band-Integrated Properties ...... 21 2.4 Determination of and Pre-Exponential Factor ...... 22 3.0 Hardware & Procedures ...... 23 3.1 Sample Material and Preparation...... 23 3.1.1 Sample Materials...... 23 3.1.2 Sample Preparation...... 25 3.1.3 Heat-Treatment Furnace ...... 27 3.2 FTIR Instruments and Procedure ...... 28 3.2.1 Integrating Sphere...... 29 3.2.2 External Sample Mounting: Normal Incidence Hemispherical Measurements...... 34 3.2.3 External Sample Mounting: ‘Forward Scattered’ Measurements...... 35 3.2.4 Internal Sample Mounting: Normal and Angular Incidence Measurements...... 37 3.3 ‘Sample Blanking’: Accounting for Light Losses, Detector & Light Source Performance ...... 40 3.3.1 Substitution Method for Outside the Sphere Configuration...... 41 3.3.2 Substitution Method for Inside the Sphere Measurements...... 44 3.4 Angled Sample Holders ...... 45 3.5 Data Reduction...... 47 3.5.1 Basic Data Reduction...... 47 3.5.2 Band-Integrated Values...... 50 3.5.3 Comparison of Surface Emittance and Absorptance from a Flame...... 51 4.0 Results & Discussion...... 53 4.1 Comparison of Inside vs. Outside the Integrating Sphere Tests...... 53 4.2 Data Sample Set ...... 54 4.2.1 Determination of Data Subset to be used for Spectroscopic Analysis ...... 57 4.2.3 Comparisons by Area Density: Normal Incidence ...... 59 4.2.4 Comparisons by Area Density: Angular Data...... 66 4.2.5 Area Density Effects on Virgin KW: Stacked Samples vs. AFP...... 70 4.3 Final Dataset Used to Represent Spectral Behavior of KimWipes® ...... 73

ii 4.4 Spectral Radiative Properties ...... 74 4.4.1 Normal Incidence Light that is Transmitted Off-Axis: ‘Forward Scattering’...... 75 4.4.2 Virgin KimWipes®: Normal Incidence...... 77 4.4.3 Virgin KimWipes®: Angular Effects ...... 78 4.4.4 Angular Dependency: The Effect of Pathlength on Radiative Properties ...... 81 4.4.5 Heat-Treated KimWipes®: Normal Incidence ...... 85 4.4.6 Heat-Treated Samples: Angular Effects ...... 91 4.4.7 Spectral Changes in the Carbonyl Band...... 101 4.4.8 Void Spaces between Fibers and their Effect on the Radiative Property Values...... 103 4.4.9 Comparison of Heat-Treated Samples with Burned Sample...... 107 4.5 Band Integrated Data Results...... 110 4.5.1 Integration of Representative Data Set...... 110 4.5.2 Example of Band-Integrated Data...... 111 4.5.3 Application of Kirchoff’s Law to Band-Integrated Properties ...... 115 4.5.4 Example Use of Band Integrated Data: Radiative Coupling...... 117 4.5.5 Narrow Band (Imaging Space) Integrated Values...... 121 4.5.6 Estimation of Temperature Errors if Incorrect Emittance Values Used...... 126 4.6 Determination of ...... 130 5.0 Summary & Conclusions...... 135 5.1 Summary of Experimental Results...... 135 5.2 Concluding Remarks...... 142 6.0 Appendix I: Basic Principles of FTIR Spectroscopy ...... 145 6.1 Overview...... 145 6.2 Advantages of FTIR vs. Dispersive Spectroscopic Techniques...... 147 6.3 Basic Principles of the Michelson Interferometer...... 149 7.0 Appendix II: FTIR Instrument Optimization Procedures and Settings..... 154 7.1 Entrance Port ...... 155 7.2 Integrating Sphere...... 155 8.0 Appendix III: Effect of Planck Curve Shift on Band-Integrated Results.... 159 9.0 Appendix IV: Experimental Uncertainty Analysis...... 162 9.1 Sample Reproducibility ...... 162 9.2 Area Density Measurements...... 165 9.3 FTIR Instrument Performance and Spectral Measurements...... 166 9.4 Activation Energy Data ...... 173 10.0 Appendix V: Complete Integrated Data Set...... 176 11.0 Appendix VI: Contact Information to Obtain Complete Spectral Data Set178 12.0 References...... 179

iii List of Tables

Page Table 1: Heat-treatment temperature, time, and area density for Case I samples………………….. 59 Table 2: Heat-treatment temperature, time, and area density for Case II samples…………………. 60 Table 3: Heat-treatment temperature, time, and area density for Case III samples………………… 62 Table 4: Heat-treatment temperature, time, and area density for Case IV samples………………… 63 Table 5: Heat-treatment temperature, time, and area density for Case V samples…………………. 65 Table 6: Subset of samples used to represent spectral property data for burning KimWipes………. 73 Table 7: Estimated total collection angle at different sample mounting distances…………………. 76 Table 8: Band-integrated emittance values of charred KimWipes at different incidence angles…… 112 Table 9: Band-integrated emittance/absorptance for KimWipes with different gas mixtures……… 120 Table 10: Band-integraed, normal incidence values for KimWipes for three spectral bands………... 123 Table 11: Change in emittance in broadband and narrow imaging bands……………………………. 125 Table 12: Temperature errors associated with using incorrect values of emittance………………….. 127 Table 13: Calculated values of the pre-exponential factor and activation energy……………………. 132 Table 14: FTIR & integrating sphere optimization parameters and results…………………………... 154 Table 15: Sample reproducibility and oven uncertainties……………………………………………. 164 Table 16: Area density uncertainty measurements…………………………………………………… 165 Table 17: FTIR instrument and spectral data uncertainty……………………………………………. 168 Table 18: Uncertainty estimates for pre-exponential term and activation energy……………………. 174 Table 19: Complete integrated data set………………………………………………………………. 177

iv List of Figures

Page Figure 1: Sources of thermal radiation in a concurrent flame spread configuration………………….. 5 Figure 2: Magnified view of virgin KimWipes……………………………………………………….. 24 Figure 3: Heat-treatment oven used for sample preparation………………………………………….. 25 Figure 4: Nicolet “Magna 760” FTIR bench, with LabSphere integrating sphere……………………. 30 Figure 5: External view of integrating sphere…………………………………………………………. 31 Figure 6: Internal view of integrating sphere………………………………………………………….. 32 Figure 7: Wedge mirror, mounted on gold arm…………………………………………………...... 33 Figure 8: Schematic layout of integrating sphere in standard (outside the sphere) configuration...... 34 Figure 9: Schematic layout of integrating sphere when used to determine ‘forward scattering’……… 36 Figure 10: Integrating sphere with spacer ring on entrance port……………………………………...... 37 Figure 11: Custom sample holders for inside the sphere tests………………………………………...... 38 Figure 12: Schematic layout of integrating sphere showing the inside the sphere configuration………. 39 Figure 13: Transmittance of virgin KimWipes, inside and outside the sphere configurations…………. 54 Figure 14: Numerical calculation of KimWipes area density vs. temperature…………………………. 55 Figure 15: Numerical calculation of area density vs. temperature, showing experimental data points… 56 Figure 16: Series of KimWipes samples heat-treated at 623 K for different times…………………….. 57 Figure 17: Absorptance of lightly charred KimWipes, Case I samples………………………………… 60 Figure 18: Absorptance of moderately charred KimWipes, Case II samples…………………………... 61 Figure 19: Absorptance of heavily charred KimWipes, Case III samples……………………………… 63 Figure 20: Absorptance of very heavily charred KimWipes, Case IV samples………………………… 64 Figure 21: Absorptance of severely charred KimWipes, Case V samples……………………………… 66 Figure 22: Absorptance of charred KimWipes, Case III samples, 45o incidence………………………. 67 Figure 23: Absorptance of charred KimWipes, Case V samples, 30o incidence………………………. 68 Figure 24: Absorptance of charred KimWipes for comparison Cases I-V…………………………….. 69 Figure 25: Magnified images of virgin KimWipes and Ashless Filter Paper…………………………... 71 Figure 26: Transmittance of 1, 2, and 4 sheets of KimWipes, and Ashless Filter Paper……………….. 72 Figure 27: Forward scattered transmittance of virgin KimWipes……………………………………..... 77 Figure 28: Normal incidence radiative properties of virgin KimWipes………………………………… 78 Figure 29: Spectral transmittance of virgin KimWipes at different incidence angles………………….. 79 Figure 30: Spectral reflectance of virgin KimWipes at different incidence angles (full scale)………… 79 Figure 31: Spectral reflectance of virgin KimWipes at different incidence angles (reduced scale)……. 80 Figure 32: Radiative properties of virgin KimWipes at 5.10 μm……………………………………….. 81 Figure 33: Variation of straight-line pathlength, as the incidence angle is varied……………………… 83 Figure 34: Area density as a function of heat-treatment time at 623 K………………………………… 86 Figure 35: Normal incidence transmittance of KimWipes, heat-treated at 623 K for varying times…... 87 Figure 36: Normal incidence reflectance of KimWipes, at 623 K for varying times (full scale)..……... 88 Figure 37: Normal incidence reflectance of KimWipes, at 623 K for varying times (reduced scale)….. 89 Figure 38: Normal incidence absorptance for KimWipes, at 623 K for varying times………………… 90 Figure 39: Magnified view of Sample 13……………………………………………………………….. 92 Figure 40: Spectral transmittance of Sample 13 at different incidence angles…………………………. 92 Figure 41: Spectral absorptance of Sample 13 at different incidence angles…………………………… 93 Figure 42: Magnified image of Sample 72……………………………………………………………… 94 Figure 43: Spectral transmittance of Sample 72 at different incidence angles…………………………. 94 Figure 44: Spectral absorptance of Sample 72 at different incidence angles…………………………… 95 Figure 45: Magnified image of Sample 82……………………………………………………………… 96 Figure 46: Spectral transmittance of Sample 82, at different incidence angles………………………… 96 Figure 47: Spectral absorptance of Sample 82, at different incidence angles………………………….. 98 Figure 48: Magnified image of Sample 29……………………………………………………………… 99 Figure 49: Spectral transmittance of Sample 29, at different incidence angles………………………… 99 Figure 50: Spectral absorptance of Sample 29, at different incidence angles………………………….. 101

v Figure 51: Absorptance in the carbonyl band for charred KimWipes………………………………….. 102 Figure 52: Void fraction as a function of area density for charred KimWipes…………………………. 105 Figure 53: Original and thresholded images of KimWipes……………………………………………... 106 Figure 54: Image of burned and quenched sample for comparison with heat-treated samples………… 108 Figure 55: Comparison of normal incidence absorptance for burned and heat-treated samples……….. 109 Figure 56: Example of broadband integrated emittance vs. temperature for different incidence angles.. 113 Figure 57: Spectral emittance of virgin and charred KimWipes, and spectral emissive power of gas…. 118 Figure 58: Calculated spectral transmittance of a representative combustion gas mixture…………….. 121 Figure 59: Calculated temperature vs. actual temperature for gray emittance approximation…………. 124 Figure 60: Example of band integrated emittance vs. temperature for different spectral bands……….. 129 Figure 61: Area density as a function of heat-treatment time for different temperatures………………. 130 Figure 62: Activation energy curve for KimWipes……………………………………………………... 131 Figure 63: Calculated burning rates for KimWipes, using previous and new values of A and E………. 133 Figure 64: Experimental thermocouple data of temperature vs. time for a burning, thin solid fuel……. 134 Figure 65: Schematic layout of Michelson interferometer……………………………………………… 149 Figure 66: Spectral emissive power and spectral emittance for KimWipes at 300 K…………………... 160 Figure 67: Spectral emissive power and spectral emittance for KimWipes at 750 K…………………... 161 Figure 68: Normal incidence absorptance for repeated tests of virgin KimWipes……………………... 172 Figure 69: Error estimation of area density vs. heat-treatment time at max uncertainty……………….. 173 Figure 70: Predicted burning rate for KimWipes using uncertainties in determining A and E………... 175

vi Acknowledgements

This work could not have happened without the help and support of many people. The following is a list of those who have contributed to this effort:

First, my wife Christine, and my kids Katie, Matthew, and Kelsey, who all sacrificed considerable time with me by allowing me to complete this work.

Todd Bartkus, for helping me get the oven (that he had previously used) set up and running; Mike Dobbs, for helping with the design of certain mechanical elements at different points; John Easton, for many discussions on a variety of topics; Ioan Feier, for providing me with numerical modeling data needed for this effort; Dr. Paul Ferkul, for many discussions on activation energy and other topics, and for proof-reading various drafts; Mike Johnston, for his excellent fabrication work on a variety of mechanical components; Julie Kleinhenz, for providing me with a combustion sample for comparison with heat-treated samples; Jack Kolis, for his support as an electronic technician in the thermal control of the heat-treatment oven; the late Professor Phillip Morrison, for many ideas and early guidance in this effort; Dr. Nancy Piltch, for guidance throughout the project and many enlightening discussions on spectroscopy and the physics of infrared emissions at the molecular level; Dr. Kurt Sacksteder, for many discussions and guidance at various stages of this effort; Peter Struk, for discussions on the presentation at the end of this effort; Kevin Tolejko, for also providing me with numerical modeling data needed for this effort; and Jim Withrow, for support on the electrical wiring of the oven and controller. The contributions that each of you provided made this a better body of work.

A special ‘thank you’ to CWRU, the National Center for Space Exploration Research (NCSER) and NASA Glenn Research Center for allowing this work. NASA also provided financial support for this work under grant NCC-633, for which I am grateful.

Finally, the help and support of Professor James T’ien, and Dr. Kenneth Street were absolutely crucial to the success of this effort. Without Professor T’ien’s patient guidance down through the years, and Dr. Street’s tireless help in the laboratory (as well as many insights into the data), this effort would have been impossible. To these two outstanding professionals, I cannot express enough thanks.

If I have left anyone off this list, please accept my apologies. All of the help, support and encouragement from everyone was greatly appreciated.

vii Radiative Characteristics of a Thin Solid Fuel at Discrete Levels of Pyrolysis: Angular, Spectral, and Thermal Dependencies

Abstract

by

RICHARD DALE PETTEGREW

Numerical models of solid fuel combustion rely on accurate radiative property values to properly account for radiative heat transfer to and from the surface. The spectral properties can change significantly over the temperature range from ambient to burnout temperature. The variations of these properties are due to mass loss (as the sample pyrolyzes), chemical changes, and surface finish changes. In addition, band-integrated properties can vary due to the shift in the peak of the Planck curve as the temperature increases, which results in differing weightings of the spectral values. These effects were quantified for a thin cellulosic fuel commonly used in microgravity combustion studies

(KimWipes®). Pyrolytic effects were simulated by heat-treating the samples in a constant temperature oven for varying times. Spectral data was acquired using a Fourier

Transform Infrared (FTIR) spectrometer, along with an integrating sphere. Data was acquired at different incidence angles by mounting the samples at different angles inside the sphere. Comparisons of samples of similar area density created using different heat- treatment regimens showed that thermal history of the samples was irrelevant in virtually all spectral regions, with overall results correlating well with changes in area density.

Spectral, angular, and thermal dependencies were determined for a representative data set, showing that the spectral absorptance decreases as the temperature increases, and

viii decreases as the incidence angle varies from normal. Changes in absorptance are primarily offset by corresponding changes in transmittances, with reflectance values shown to be low over the tested spectral region of 2.50 μm to 24.93 μm. Band-integrated values were calculated as a function of temperature for the entire tested spectral region, as well as limited bands relevant for thermal imaging applications. This data was used to demonstrate the significant error that is likely if incorrect emittance values are used in heat transfer calculations. The pyrolyzed samples were also used to determine the activation energy and pre-exponential factor needed in the zeroth-order Arrhenius reaction, sometimes used to model the mass loss from the surface in numerical models.

The values determined were used to calculate an estimated peak surface temperature, which agrees well with experimentally determined values.

ix 1.0 Introduction

Knowledge of the combustion process is a crucial step in the design of safe and effective spacecraft and space habitats. Combustion can play a significant role in multiple design aspects, including propulsion, power generation and fire safety. Accordingly, great efforts are ongoing to understand the combustion process from both a fundamental and applied standpoint. The history of manned spaceflight has shown that lack of understanding of the combustion process, particularly in the area of fire safety can lead to catastrophic results, as evidenced by the Apollo 1 tragedy and the 1997 fire aboard the

MIR spacestation1

Heat transfer, in various forms, is a fundamental process in combustion. Understanding the role of each of the modes (convection, conduction and radiation) of heat transfer is a crucial step in comprehending the combustion process. The relative importance of each of these heat transfer modes can change from one configuration to the next, depending on geometry, flame configuration, etc. While each of the heat transfer modes can be important, this discussion will be limited to the role of radiation heat transfer, and issues relevant to such radiation.

1 1.1 Radiative Heat Transfer in Combustion Problems

Thermal radiation heat transfer plays an important role in many problems involving the combustion of solid . For many burning solids, the surface temperature is high (500-

800K) and surface radiation loss contributes a significant portion of the surface energy balance for determining the burning rate. When convective velocity drops below the normal-gravity buoyant-induced limit (i.e. in the sub-buoyant flow regime), combustion intensity is reduced and radiative loss becomes important. At sufficiently low convective velocities, radiation not only affects the flame behavior, but can also affect the viability of the flame. For example, radiative loss can induce a quenched extinction in a low-speed flow1. The quenching limit induced by radiative heat loss has many opposite characteristics compared with the high-speed blow-off limit2,3,4, including lower surface and flame temperature (in the radiative quenching case), reduction in soot, and change of flame structure.

The effect of radiative loss is illustrated using a computed result from a flame-spread model in low-speed concurrent flow over a thin solid1,5. In this computation, the surface is assumed to be a gray body with equal emittance* and absorptance. Results from this computation show that flame spread rate is sensitive to the value of emittance assumed.

* The different suffixes used to describe the radiative properties (e.g., emittance or emissivity) are often used interchangeably in the literature. Incropera and DeWitt6 state “efforts are being made to reserve the – ivity ending for optically smooth, uncontaminated surfaces…”. On the other hand, Siegel and Howell7 define emissivity as “the property of a body that describes its ability to emit radiation as compared with the emission from a blackbody at the same temperature”, but then define emittance as “the property of an isothermal material that describes the ability of a given thickness to emit energy as compared to emission by a blackbody at the same temperature”. In this work, the convention of Siegel and Howell is used, and since all materials studied were of finite thickness, all property values will be referred to using the ‘ance’ suffix.

2 When emittance is increased from 0.4 to 0.8, for example, the spread rate is reduced by about 50%. Low-speed quenching limit is even more sensitive to the value of surface emittance.

Flame radiation not only is a loss from the flame but also constitutes an energy feedback mechanism for pyrolyzing the solid fuel ahead of the flame. Recent activities (both numerical and experimental) in microgravity combustion and spacecraft fire safety further demonstrate the importance of radiation as a feedback mechanism4,8,9. Because of its importance, many recent modeling works on solid combustion have included surface radiation alone or surface and flame radiation together1,10,11. Some efforts have included gas-phase radiation as a heat-feedback mechanism to the solid surface, using narrow- band gas emission models10,11. The accuracy of these efforts suffered from lack of temperature and spectrally dependent surface properties*, to allow calculation of absorption, reflection and emission by the surface.

The difficulty in proper treatment of radiation heat transfer lies in the complexity of the problem. Accurate modeling requires knowledge of optical properties of all the participating media, temperature, chemical composition and/or concentration of the participating media, path lengths through which the radiation is acting, and view/shape factors between the bodies or elements that are radiatively interacting7,13. The scope of the modeling problem, especially when all of these parameters are considered in multiple

* The term “radiative properties” is used throughout the course of this work to refer to the radiative characteristics of the given media. Moran and Shapiro12 define a quantity to be a property “if, and only if, its change in value between two states is independent of the process”. The question will be raised, and subsequently answered, as to whether this definition holds true for the radiative characteristics of the sample material tested here. However, the convention of referring to the radiative characteristics as ‘properties’ is used throughout this work.

3 spatial dimensions, is obvious. Computational constraints have long placed limits on the degree of sophistication of numerical combustion codes. While this problem is steadily improving due to technical improvements in computing technology, simplifications are still generally required to provide acceptable computational time. A common example of this has been the assumption of one or two dimensional flame fronts5. By assuming symmetry and reducing the physical degrees of freedom of the problem, considerable computational savings are realized. This is particularly true with regards to radiative heat transfer, where energy exchange from virtually any point in the computational domain can take place with nearly any other point.

The need for an understanding of some of these parameters and their effects on the combustion process is the motivation behind this work, which is an effort to characterize the radiative properties of a class of thermally thin*, solid fuels. However, to clearly understand the nature of the problem and the need for its resolution, some effort must be made to understand the current state of work in combustion related radiation heat transfer, with regard to both gas-phase and surface radiation.

1.2 Gas-Phase Radiation

Unlike flames in normal gravity where gas-phase radiation becomes significant only in large flames14, gas-phase radiation in microgravity can be important in smaller flames4 .

* The term ‘thermally thin’ refers to a classification of materials in which the rate of conduction of energy into the depth of the fuel is great compared to the rate of conduction of energy in the length direction. This means that there is no temperature gradient in the depth of the fuel, i.e., the material is isothermal in the depth direction at any given point.

4 In the recent modeling efforts on solid combustion in microgravity, flame radiation has

5,10,15,16,17 been incorporated . The radiating media in general include CO2,H2O, fuel vapor and soot. Figure 1 shows a schematic representation of how radiation from the concurrent flow, gas-phase flame can be both a heat feedback mechanism to the solid, and a loss mechanism.

Thin Solid Fuel

SurfaceSurface radiation, radiation, Gas-phase radiation, absorbedabsorbed by by the the flame, reflected off the fuel andflame lost andto the lost to the environmentenvironment

Gas-phase radiation, Gas-phase radiation, transmitted through absorbed by the fuel, and the fuel lost to the environment

Figure 1 Sources of thermal radiation in a concurrent flame spread configuration.

Near the quenching limit, soot is absent so the radiating media are only the gaseous species. Gas radiation is known to be highly spectral. To account for the gas radiation accurately, a narrowband model has been employed in one-dimensional flames10,15.

Narrowband data for gaseous species is available from a number or sources, e.g., the

HITRAN and HITEMP databases. These databases were compiled for common atmospheric and combustion gases, such as CO, CO2 and H2O (as well as others) so that spectrally resolved data can be determined for each gas as a function of concentration, path length, and temperature (within some limits).

5 On the other hand, the gray-gas model is still being employed in multi-dimensional problems such as flame spreading over solids because of the limitation of computational resources1,5,7. Although unable to resolve the flux on a line-by-line spectral basis, these works strove to obtain a reasonably accurate total radiative heat flux at the solid boundary by various types of approximations.

1.3 Surface Radiation

Understanding the optical properties of a solid fuel is important to both modeling and experimental work. From a modeling perspective, the ability to calculate energy transfer at the solid surface can be achieved with knowledge of its broadband emittance and absorptance characteristics. However, calculation of its ability to radiatively interact with the gas phase is dependent on knowledge of the spectral characteristics of the surface.

Characterizing the overall radiative properties of a solid is generally more complicated than characterizing those of a gas, for several reasons. The gas mixture can be dealt with by considering the constituents individually; the spectral and thermal dependence on the emission (or absorption) is known for most gasses. Also, gasses can be considered non- reflecting. This simplifies the conservation of energy equation as it relates to the material

(τ+ ρ+ α= 1, where τis the transmittance, ρ is the reflectance, and αis the absorptance), meaning that energy which is not transmitted can be assumed to be absorbed. Further, there is no viewing angle dependence in gasses, and the constituents

6 can generally be assumed to be chemically unchanging. Certain difficulties remain, particularly the path length, concentration and temperature distribution, but these issues may be relevant in some form to both solid (if the material is neither optically thin nor thick) and gas radiation.

1.3.1 Reasons for Spectral Dependence

In contrast to the case of gas phase radiation, the solid presents additional challenges to accurate radiation modeling. Most solids exhibit a spectral nature to their radiative properties, yet these properties generally do not have the sharp, well defined spectral properties found in gasses. There are several reasons for this spectral ‘smearing’ of the solid optical properties.

One of the reasons for the broad spectral response of most solids lies in the molecular structure of the material. Infrared photons are emitted when a molecule loses energy in one or more vibrational modes. The number of ways in which a molecule can vibrate can be quantified with the simple expression seen in Equation 1:

# Vibrational Modes = 3n – 6 Equation 1

In this expression, ‘n’ is the number of atoms in the molecule (this expression is true for molecules that are nonlinear in their structure; for linear molecules, the proper expression is 3n – 5). In each vibrational mode, there are discrete quantum energy levels that the

7 molecule can possess18. When the molecule emits or absorbs energy, it must do so between these discrete energy levels. These transitions between energy levels correspond to frequencies at which infrared energy is released or absorbed. These different transitions are why even a simple molecule such as CO2 can emit or absorb at multiple locations in the spectrum. Large hydrocarbons with many atoms will have a vast number of possible vibrational modes. For example, a simple hydrocarbon such as CH4 will exhibit 9 modes, while cellulose (C6H10O5) will have 57 modes. In addition to their fundamental modes, harmonics will also exist in which transitions are made across multiple levels, further adding to the spectral signature.

Another reason for the broad spectral response of solids lies in their density. In the solid phase, molecules are packed relatively close together, which means that these individual molecules can exchange energy with each other. As each molecule is vibrating, some of its atoms can interact with atoms of neighboring molecules, causing energy transfer to the neighboring molecule. This will cause further ‘smearing’ of the spectral properties for the solid. This phenomenon is also seen with gasses, where high pressure causes a broadening of the spectral bands.

1.3.2 Temperature Dependence & Thermal Effects

The wide temperature ranges encountered in combustion processes will affect the optical properties of the surface. The increasing temperature can alter these optical properties in multiple ways. First, the band-averaged property values will be changed because the

8 peak in the thermal emissions shifts to shorter wavelengths with increasing temperature.

Since the optical property values are spectral in nature, the relative weighting of contributions by different spectral absorption bands to the material’s band-averaged emittance will change as the temperature changes19,20.

An indirect temperature effect is that solid fuels will pyrolyze in the presence of elevated temperatures. As the material temperature rises, volatiles are lost from the fuel, meaning that the material which remains will have a different chemical composition than the original ‘virgin’ material. Additional consequences of pyrolysis are that the material thickness will decrease as it ejects pyrolytic gasses, and the surface topography may change. If the surface is optically thick to begin with, the decrease in the fuel surface may or may not be significant, but in many practical combustion fuels such as paper or some cloths, the material is neither optically thin nor thick. For materials that are neither thin nor thick (optically), transmittance will be a function of thickness. This is analogous to the path-length dependence seen in gasses. Regardless of whether the material is optically thin, thick, or neither, the surface finish will always have an effect on the optical properties.

These pyrolytic effects will occur at elevated temperatures, regardless of the environment which the material is in. However, if the material is pyrolyzed in the presence of oxygen, oxidation will take place. This will also serve to change the chemical makeup of the material, with different spectral properties.

9 1.3.3 Angular Dependence

In addition to temperature and spectral dependence, the optical properties of many solids also display an angular dependence. Knowledge of this angular dependence is vital for accurate numerical modeling, as each point on the material surface will experience energy exchange with its surroundings in all directions.

1.4 Radiative Interaction between Gas and Solid

Radiation from the gaseous flame can be partly a heat loss and partly an energy supply back to the surface to vaporize the fuel (i.e. radiation absorbed by the solid). Because of this close interaction between the gas and the solid, the model with a detailed gas radiation formulation will not have a consistent level of accuracy unless the solid spectral properties are included. The reason for this is conceptually simple: the effectiveness at which the surface absorbs radiation can be wavelength dependent. Since the incoming radiation from the gas phase is also highly spectral, a large amount of incoming energy will not be absorbed if the spectral range of that incoming radiation does not coincide with absorption bands in the solid. A similar argument can be made with regard to the outgoing radiation from the surface, and absorption by gas phase constituents20,21.

Another point is that the spectrally averaged emittance and absorptance do not have to be the same at the surface. The source of infrared emission for a burning solid is at the surface temperatures up to a few hundreds degree Kelvin while for absorption, the source

10 is at the flame temperature, which could be as high as about 1500 to 1800 K10,11. The consequence of this disparity was explored by assuming different combinations of emittance and absorptance, with interesting results21,22. For example, if surface absorptance is large but emittance is small, the burning rate or the spreading rate can exceed their corresponding values in the adiabatic limit. Therefore, the overall accuracy of models that have narrowband gas phase radiation (or, in the future, line by line models) will be compromised unless the spectral properties of the surface are well known.

1.5 Previous Knowledge of Optical Properties

Historically, radiative properties have been treated in one of two ways. The first is to assume blackbody properties, i.e. ε= 1 (where εis the emittance). This approach has been used in both modeling and thermal imaging applications11,25,26. While this approach side-steps the need to understand the thermal, spectral and angular dependence on the optical properties, it does so at the expense of accuracy. By assuming ε= 1, the actual temperature of the solid will be under predicted (for the same radiative heat flux). The amount of the error depends on both the degree of inaccuracy of ε, and on the temperature itself. For example, if the true temperature is 400 K and the true emittance is

0.8, using a value of ε= 1.0 would lead to an error of about 22 K. If the actual emittance were 0.6, using ε= 1.0 would cause an under prediction of 48 K. The effect of temperature on the error is seen by considering the same cases at a higher temperature.If

11 the true temperature of the surface is 600 K, and the actual emittance is ε= 0.8, using the blackbody assumption will lead to an underestimation of about 33 K. If the actual emittance (of the 600 K target) is ε= 0.6, the error will increase to about 72 K.

The other approach commonly used has been to assume a non-unity, but constant (gray) value for ε. As an example, one of the most referenced solid fuels used in the laboratory studies is cellulosic paper, which is a typical thin solid fuel. The emittance of paper is listed in standard texts7,6. Reference data (at 310 K) are given as =0.91 for roof paper and =0.95 for white paper. The values of radiative property values found in the literature are typically measured at one wavelength or represent a spectral average over a narrow waveband (often in the visible spectral region), one temperature, and one viewing angle. This simple listing implies that paper can be regarded as a gray radiation medium.

In addition to its limitations at a single temperature, wavelength/waveband, and viewing angle, this data made no mention of the dependence of paper thickness. Further inaccuracy results in the case of a burning fuel surface, where thermally induced changes

(pyrolysis, oxidation, and change in thickness or surface finish) are not accounted for.

Attempts have been made to determine the radiative properties for some materials, over some range of conditions. For instance, several studies have examined the spectral nature of metals over a moderate range of temperatures, for application to metal extrusion and fabrication processes27,28. Other methods have been developed for determining gray emittance values of materials at ambient or near ambient temperatures29, but none of

12 these approaches address the changing nature of the radiative properties of a burning surface, either spectrally or broadband.

Some work has been done to characterize the narrowband emittance of solid fuels that are undergoing pyrolysis30,31. The surface emittance was measured to allow radiometric thermal imaging of the fuel surface through a flame, employing a narrow spectral band in which gas emissions were minimized. While useful for thermal imaging of the burning surface, the narrow spectral nature of these results give almost no information on the overall radiative nature of the surface.

Recent efforts have been made to address these problems using different methods. Using a Fourier-transform infrared (FTIR) spectrometer with an integrating sphere enabled the spectral dependence of the radiative properties of a variety of samples to be measured hemispherically32, for materials at room temperature. Serio, et. al. developed an instrument to allow measurement of the radiative properties of certain charring materials as they are being heated33, but this device was limited to making measurements at near normal viewing angles.

1.6 Objectives of This Study

The current work is an effort to extend the understanding of radiation from a solid by determining the spectral, angular and thermal dependence of the radiative properties of several thin solid fuels currently used in combustion studies. This work has proceeded in

13 stages, with specific efforts aimed at understanding the thermal and spectral dependencies of specific fuels and the implications of this with respect to the broadband properties20, 34, then concluding with the determination of the angular dependence of these properties.

The sample material selected for this study was KimWipes®. This paper fuel was selected because of the body of experimental and numerical data previously collected by many researchers using this or similar fuels1,5,8,21,25. The techniques and methodology developed will be applied at a later date to a custom woven cloth, which is scheduled to be used in an upcoming reduced gravity combustion experiment35. The approach to this work involved using an FTIR spectrometer to determine spectral dependence combined with an integrating sphere, similar to the work of Hanssen32. The integrating sphere is required to capture all of the reflected and transmitted energy from these diffuse fuel samples. The thermal effects were captured by pyrolyzing samples in a furnace (at varying temperatures and durations) prior to making the spectral measurements. The angular dependency was accounted for by repeating the measurements at a range of discrete angles (also using the integrating sphere). The total data set then allows the spectral evaluation of the radiative properties at a variety of char conditions and viewing angles.

The spectral data is then used to evaluate the broad-band property values as a function of temperature, and sample calculations were made to illustrate the radiative interaction between a heated gas mixture and the fuel surface. This clearly shows that the broad- band emittance and absorptance values can be quite different, due to the differences in

14 the spectral properties of the surface and the gas, and their different temperatures. The data also allows the calculation of the narrow-band emittance values, which allows the determination of the solid temperature at different viewing angles using in radiometric thermal imaging.

Finally, the pyrolyzed samples were used to calculate values for the activation energy and pre-exponential factor used in a zeroth order pyrolysis model, of the type commonly used in numerical models. The combination of better values for these numerical parameters, along with the improvements in heat-transfer calculation accuracy brought about by the spectral results of this work should lead to meaningful improvement in the accuracy of the numerical combustion codes that model such fuels.

15 2.0 Experimental Approach & Overview

The approach used in this work is to experimentally determine the radiative properties of a thin solid fuel, with respect to spectral, angular, and certain thermal dependencies.

Moreover, this effort is aimed not only at determining the property values for this particular material, but also to develop a general methodology by which the radiative properties of other thin, solid fuels may be evaluated.

2.1 Premise and Assumptions

The basis for this effort is the premise that the thermal, spectral, and angular dependence of the radiative properties of a combusting solid fuel can be accurately captured in an experiment in which the sample is not being burned. Rather, this experiment assumes that pyrolytic effects (which themselves are caused by elevated temperatures) are captured by studying samples pyrolyzed at discrete levels, and spectroscopically studied at ambient temperature. This is required, as these properties can only be measured properly using an interferometer and an integrating sphere, devices which are, in general, not amenable to use with a burning sample.

Several assumptions are required to carry out such measurements. The most important assumption is that on the spectral level, the data would not intrinsically change if the

16 spectrum were measured with the sample at elevated temperature. While this assumption may not be strictly true, it is required due to the experimental setup.

Some work has been done to quantify the effect of elevated temperature on the emittance of materials such as metals, at temperatures low enough that they did not experience phase or chemical changes. Haugh27 showed (experimentally) that for aluminum samples, the emittance at 2 μm increases by about 5%, between 600 K and 700 K. The theoretical basis for the emittance increase in metals is the interaction between an electromagnetic wave and the free electron cloud in the metal. In a dialectric (such as the cellulose material considered here), this effect could potentially be much smaller.

The basic assumption that the spectral data would not be significantly altered by elevated temperature still allows one aspect of temperature dependence to be captured for band integrated data. For such data, the changing shape of the Planck curve (whose peak moves to shorter wavelengths as the temperature increases) itself causes a temperature dependence. This effect is investigated in this effort.

Another assumption made is that the area density of the material is a monotonic function of temperature. This assumption is evaluated through the course of this work, and is discussed later. One reason why this assumption may not be strictly valid is if the sample were to initially contract upon being exposed to heat treatment, which could cause an increase in the measured area density, until the pyrolytic decay process would begin to dominate. During that brief period of increased area density, the absorptance of the

17 material would be expected to increase, with the transmittance decreasing. However, this effect is likely to be small, and can be evaluated with the experimental data.

Other assumptions are made through the course of this work. These assumptions lie primarily in the realm of experimental methods and errors, and as such are not fundamental to the overall scope of the work. These assumptions will be addressed throughout the work, and particularly in Appendix IV, which deals with experimental uncertainty.

2.2 Data Acquisition and Determination of Spectral Properties

The sample material (KimWipes®) examined in this work is a thin cellulosic material which is commonly used in combustion studies. This fuel is considered thermally thin, meaning that no thermal gradient will occur in the thickness of the fuel in typical flame spread experiments1,14.The fact that it is thermally thin is why it is referred to as a ‘thin’ fuel, but from a radiation heat transfer standpoint this material is neither optically thin nor thick.

The approach for the determination of the spectral properties of this ‘thin’ solid material

(and their dependence on temperature and viewing angle) involved the use of an FTIR spectrometer with an integrating sphere. One configuration of the experiment was to measure the sample’s spectrally resolved reflectance (λ), and its spectrally resolved transmittance (λ) at a normal viewing angle and at constant temperature. This, combined with an appropriate statement of conservation of energy, allows the calculation

18 of the absorptance, α(λ). Through Kirchoff’s Law, the absorptance is equal to the emittance (at the same viewing angle, temperature, and wavelength)*.

The angular dependence of the spectral properties was determined using a novel re- configuration of the integrating sphere. Samples were mounted inside the sphere on customized holders at a series of discrete angles with respect to the incoming radiation

(normal use of the sphere involves mounting the samples either at the entrance aperture or at a reflection measurement port built into the bottom of the sphere), giving measurement of the hemispherical transmittance and hemispherical reflectance.

Interpolation can then be done to estimate property values at angles not tested.

In-situ measurement of samples at elevated temperatures was not possible, due to physical limitations of the FTIR and integrating sphere systems. FTIR instruments, by their nature, are sensitive to thermal changes (both in terms of the interferometer parts and the infrared detector), and are generally used in temperature controlled conditions.

The integrating sphere is made of gold-plated plastic, and would therefore not tolerate elevated temperatures. Further, the pyrolytic gasses ejected from a heated sample would foul the inside of the sphere, changing the internal background reflectance of the sphere and therefore alter the measurements themselves.

These limitations were addressed by heat-treating samples in a separate furnace, for a variety of fixed temperatures and time durations. The furnace had a normal air

* The total absorptance is often different from the total emittance, because spectral and temperature differences between the radiative participants cause the integrated values to differ, without violating Kirchoff’s Law. This phenomena is described in detail in Section 4.5.1.

19 environment, so samples were exposed to oxidative effects during the heat treatment.

These samples were then cooled to room temperature, and area and mass measurements were made to determine their area density (due to difficulty in accurately measuring the thickness of such dimensionally thin samples, they are classified in terms of ‘area density’*, rather than the typical volumetric density). These heat-treated samples were then spectroscopically examined as previously described.

Finally, some insight was gained into the angular behavior of light which was transmitted through the sample. This was termed ‘forward-scattered’ transmittance fs(λ), defined as light which is transmitted through the sample off axis from the incoming beam. The thin cellulosic materials used in this work are composed of a ‘mat’ of interlocking fibers with gaps between the fibers. The measured spectrum represents a spatial average over this inhomogeneous structure*. The transmitted light can then have two components: a part directly passing through the ‘gaps’ between the fibers, and a part transmitted through the fiber after a fraction was absorbed by the material. Similarly, the ‘forward-scattered’ light can be composed of light which is reflected off of fibers into a generally ‘forward’ direction, or light which passes through the fibers but is refracted off axis due to changes in the index of refraction. No attempt was made to separate these effects, except for the classification of (nominally) direct transmittance versus ‘forward-scattered’ transmittance.

* All area density measurements in this work are made with respect to the full thickness of the material. * The spectrometry measurements made in this study employed a light beam that was approximately 1 cm in diameter on the sample. Therefore, the spectral data represents an average over an area of about 0.8 cm2.

20 2.3 Determination of Band-Integrated Properties

The total emittance is defined as the ratio of the actual spectrally-integrated radiation emitted from an object to the spectrally-integrated emissions from a blackbody at the same temperature (similarly for other radiative properties). To calculate this quantity, the spectrally resolved data was multiplied (at each spectral data point) by the Planck curve to give a spectrally resolved flux. This flux was then integrated with respect to wavelength and ratioed with the spectrally-integrated blackbody flux calculated at those same temperatures to yield the band-averaged (or ‘total’) property values at that temperature. The process was then repeated using different temperatures in the Planck calculations, to yield the temperature dependence over the entire (tested) spectral domain.

Since the peak of the Planck curve shifts with temperature, the relative importance of the spectral data shifts with temperature19,20. This effect was examined over the broad spectral band that was tested by applying the entire data set (unpyrolyzed and progressively pyrolyzed samples) to Planck curves of varying temperatures, and calculating the total emittance in each case. Similar methods were used to determine the narrow band emittance values, for use in radiometric thermal imaging of the sample surface during combustion.

An external high temperature spectral flux is needed to obtain the total absorptance by the solid fuels in a combustion environment. The externally applied flux was chosen to correspond to that from H2O and CO2, in conditions typical of those found in the

21 concurrent flow flame spread condition, and was determined using an existing numerical model of a concurrent flow flame5.

2.4 Determination of Activation Energy and Pre-Exponential Factor

The large sample set created for use in determining the radiative properties also enabled the determination of the activation energy and pre-exponential factor for this material.

Samples were created by heat-treatment at one of four discrete temperatures for varying periods of time, which enabled the simple determination of the rate of mass loss as a function of time. This rate of mass loss can be interpreted as the ‘pyrolysis rate’, allowing calculation of the activation energy and pre-exponential factor for a zeroth order

Arrhenius pyrolysis model. Justification of the zeroth order model is provided by the observed behavior of the mass loss as a function of time.

22 3.0 Hardware & Procedures

3.1 Sample Material and Preparation

The spectroscopic procedures described are applicable to any thin solid material that chars during pyrolysis, or materials that melt but are solidified into a thin solid. For example, thin samples of PMMA could be examined after being exposed to a flame or other heat source, provided that the sample was permitted to cool and re-solidify into a thin slab.

The materials used in this study were thin cellulosic samples, which exhibit charring behavior when exposed to heat. While the procedures describe the use of the specific sample materials chosen for this experiment, they are relevant to any of the wider class of thin solid fuels that char, such as many fabrics, thin slabs of wood, etc.

3.1.1 Sample Materials

The sample material studied in this work is primarily KimWipes® (a common thin laboratory wipe manufactured by Kimberly-Clark), a thin fuel often used in solid fuel combustion studies. Ashless Filter Paper® (another common laboratory paper product, manufactured by Whatman) was also used for a limited number of comparison tests.

KimWipes® are a thin, cellulosic tissue paper that consists of 99% cellulose with 1% polyamide resin, having an average area density of 1.85 mg/cm2, based on full-thickness

23 of the fuel. This fuel is made of individual cellulose fibers that are irregularly woven into an interlocking mat (Figure 2). This material has been used extensively in both experimental and numerical microgravity combustion studies1,5,35,37 because it is thin enough to allow significant flame propagation in the relatively short test times that are often available in ground-based microgravity tests. Techniques for the current work were developed using KimWipes® because the extensive body of work which has used this fuel can benefit from the development of this data.

100 microns

Figure 2: Magnified view of virgin KimWipes®, showing fiber structure and gaps between fibers.

Ashless Filter Paper® was briefly examined as an example of a paper fuel with a greater area density (8.56 mg/cm2, also based on full-thickness) than that of KimWipes®. This material (specified as grade 1 ashless filter paper) is manufactured by the Whatman

Corporation, and has also been used in previous microgravity studies38. The structure of this material is much finer than that of KimWipes®, with the individual fibers being much finer in size and packed much tighter. The result of this finer structure is that there

24 are substantially less gaps between fibers and virtually no direct light path through the sample without striking a fiber.

3.1.2 Sample Preparation

Samples were prepared by cutting the cellulosic materials into sections approximately 8 cm x 5 cm. These samples were then clamped into a sample holder frame, which was then mounted on the furnace carriage (Figure 3). After the furnace was preheated and stabilized at the desired temperature, the sample carriage was manually moved into the furnace cavity for the desired heat-treatment time. Timing of the sample heat-treatment was done manually, with a stopwatch.

Oven

Sample, mounted on carriage

Figure 3: Heat treatment oven used for sample preparation, showing sample mounted in frame on carriage.

25 After removal and cooling of the sample, the sample was trimmed to remove the edges that were constrained in the sample holder-clamp, as these areas were conductively cooled by the sample holder and did not experience the level of pyrolysis that the exposed sample did. The samples were trimmed in such a way that only regions of visually-similar color and texture were retained, as best possible. This trimmed sample was then weighed on an analytical balance, to a precision of 0.002 mg.

Initial area measurement of the trimmed samples was made by photo-copying the sample, then carefully cutting out and weighing the blackened area of the photocopy. The ratio of the mass of this cut-out to the mass of the original 8.5” x 11” sheet (previously weighed) was proportional to ratio of the area of the cut-out, relative to the area of the original sheet. Since the area of the original (rectangular shaped) sheet was easily determined, this method allowed accurate determination of the area of the irregularly shaped samples, after they were trimmed (assuming uniformity in the area density of the copy paper).

This method was used to give an initial indication of the area density prior to the spectroscopic testing, which was a useful guideline for which samples to test.

The samples were then trimmed into approximately circular shapes to allow them to mount onto the sample holder, with no overlap. This meant that the sample which was tested was actually a small subset of the original sample. While every effort was made to select a region of the sample that appeared visibly uniform (with respect to color and surface roughness), a modest degree of sample non-uniformity was noted to exist.

26 Therefore, the area density of the smaller, trimmed sample piece that was spectroscopically examined was verified after the FTIR examination. This minimized area density measurement error due to non-uniformity of the overall sample. Any spatial non-uniformity that remained after trimming to the final sample size is indistinguishable, and the final data must be regarded as representative of samples with that average area density, as confirmed by duplicate testing.

3.1.3 Heat-Treatment Furnace

All samples were heat-treated in a small, isothermal oven that was previously used in a different microgravity combustion experiment40. The furnace was DC powered, controlled with a PID controller (using an embedded thermocouple as feedback) to a maximum temperature of 1000 K. This furnace was cylindrical, measuring 8.9 cm internal diameter and 9.1 cm internal height. The furnace was mounted on an insert for use in a drop-tower experiment rig, and was equipped with rails which allowed a carriage to slide the sample in and out of the heated area (Figure 3). This feature was particularly important because it allowed controllable and repeatable sample placement and heating times for the samples, to within one second resolution.

27 3.2 FTIR Instruments and Procedure

3.2.1 FTIR Spectrometer

The spectrally resolved data in this work was acquired using a Nicolet “Magna 760” 

FTIR (Fourier Transform Infrared) spectrometer with a DTGS (deuterated triglycine sulfate) detector (mounted inside an integrating sphere, discussed in Section 3.3). The

FTIR is a bench-top device, with a small sample compartment of 9”x 7”x 10” in which to mount either the sample itself, or an integrating sphere. Spectra were acquired between

400 and 4500 wave numbers (cm-1)* at 8 cm-1 data spacing, though the final data set has the wave number range truncated due to noise in the spectral extremes, using only from

455 to 3671 wavenumbers. For the final data set, 250 scans were averaged for each spectrum. The radiation source for the FTIR comes from a heated ceramic glow-bar, with a temperature of 1520 K. The emissions from this source are not collimated, but converge to a minimum spot size then diverge. The amount of light, the diameter of the beam and the divergence angle of the beam are controlled by an aperture on the FTIR instrument (also referred to as the ‘bench’). A general discussion on the working principles of the FTIR interferometer is contained in Appendix I.

* Spectroscopists tend to refer to spectral units of wavenumbers (cm-1), while many engineers prefer to work with wavelength units (typically, μm in the infrared, or nm in the visible region). The spectroscopists’ preference is probably because the distribution of energy is linear with wavenumbers, while the engineers’ preference probably stems from the fact that the Planck function is commonly presented in engineering texts in terms of wavelengths. In this instance, the wavenumber is presented because this is the way that the spectral range and resolution are specified with the FTIR device. Throughout most of the results section of this work, the wavelength presentation is used, as this is likely to be the preferred nomenclature of the intended reader.

28 Various configurations of aperture settings, number of scans, wavelength resolution, and instrument parameters were examined to determine optimal settings and configurations in which to acquire correct, high quality spectra. The previously noted conditions were selected as the optimal settings and conditions. Details of how these optimizations were determined can be found in Appendix II.

Further, special procedures were employed to account for light losses in the sphere, detector and light source performance, and other factors which must be considered when collecting optical constant data. Collectively, these procedures establish a baseline data set against which the sample data is ratioed. This process is referred to as “collecting a background” data set, or “sample blanking”. These procedures were somewhat customized for each of the configurations, and are described in detail in Section 3.3.4.

3.2.1 Integrating Sphere

Integrating spheres are used to capture the hemispherical reflected or transmitted light from diffuse targets, so that all of the reflected or scattered energy is collected. These devices range in size from inches in diameter to several feet or more in diameter, depending on the type of tests to be performed. The sphere used in this effort was a small, bench-top model designed to fit into the test compartment on the Nicolet “Magna

760” FTIR instrument (Figure 4). This sphere was used in several configurations in this study, to allow acquisition of spectra at different incidence angles, and to make a limited estimation of the angles at which light is “forward scattered” (i.e., transmitted through the

29 Integrating Sphere

Figure 4: Nicolet® “Magna 760” FTIR bench, showing the LabSphere® integrating sphere installed. sample but deflected off-axis). Some aspects of these configurations were custom built for this application; as such, each of these configurations will be discussed in detail in

Sections 3.2.2 through 3.2.4. The sphere (used in all configurations) was produced by

LabSphere, Inc., and is comprised of a plastic shell with a diffuse gold internal coating.

An external image of the sphere is shown in Figure 5. The internal diameter of the sphere was 7.62 cm. The sphere contains its own detector (previously mentioned) and light baffles*, and has an entrance aperture (not to be confused with he previously mentioned bench aperture) of 16.3 mm diameter where samples can be mounted for normal incidence measurements of hemispherical transmittance and an exit aperture of 19.1 mm where hemispherical reflectance can be determined. Aperture plates were used to stop down these ports when mounting the samples inside the sphere. The larger ports were used with the outside the sphere configuration to allow a greater throughput of energy,

* Light baffles are needed to prevent any incoming light from entering the detector after only a single reflection, so that all light that is eventually collected will have been attenuated a similar amount (more or less) by the small absorptive losses that occur each time some of the light is reflected off the sphere’s inner surfaces.

30 since only uncharred samples were used in this configuration (these samples were taken to be spatially uniform). Smaller apertures (12.5 mm entrance, 9.3 mm exit) were used for the inside the sphere measurements, since small sample pieces were selected for their

(apparent) spatial uniformity, and the beam size needed to be no larger than the sample size. By insuring that the beam size was smaller than the sample (and centering the sample with respect to the beam), the mounting tape that was used to hold the sample to the sample holder was outside of the incoming beam, preventing it from adding to the spectral signature of the sample.

Viewing port where samples were mounted for inside the sphere tests

Entrance port, with external aperture

Figure 5: External view of integrating sphere, showing entrance aperture plate used in angular measurement tests

A turning mirror is provided internal to the sphere, which can be set to either redirect the incoming beam down onto the a sample mounted at the reflection port (about 80o angle relative to the sample plane), or it can be rotated to direct the beam onto the interior of the sphere when the reflection port is not used (in one of the configurations, the turning mirror was replaced entirely, discussed later). This turning mirror was used in all tests

31 conducted with the sample mounted outside the sphere (i.e., the ‘typical’ configuration in which integrating spheres of this type are commonly used). An additional viewing port is also provided near the top of the sphere (seen in Figure 5 and Figure 6), which can be opened to visually inspect the placement of the sample when mounted in the reflection port (this viewing port was also used to mount the custom sample holders used in the angular measurements). Figure 6 shows an image of the inside of the disassembled sphere.

Turning mirror Entrance Port Light Baffles

Detector Port Exit Port Detector

Figure 6: Internal view of integrating sphere. Front half of sphere (on left side) has been rotated away from the back half for illustration.

Initial testing showed that light losses due to first reflection off of the back of the sphere are significant, and would lead to underestimation of light transmitted through the sample. This discrepancy was noticed in early tests between normal incidence transmittance between the inside the sphere and outside the sphere methods. Part of the solution to this was to use a custom made “wedge mirror”(Figure 7) to deflect the incoming beam at angles away from the sample, for the tests conducted inside the sphere.

32 Apex of mirror is rotated 5 degrees clockwise from vertical

12.0 mm

11.4 mm

Apex of triangle is 8.3 mm from base Figure 7: Wedge mirror, mounted on gold-plated arm. The rectangular piece on the left is the selector arm, normally used to position the turning mirror seen in Figure 6. This piece was used to position the wedge mirror directly in the beam path. This mirror (measuring 12.0 mm by 11.4 mm on each face, with an apex of 8.3 mm) was subsequently used in all tests conducted inside the sphere, both normal incidence and at different angles. The mirror was mounted with its apex tilted clockwise (as seen though the entrance port) by 5 degrees, to prevent direct reflection into the detector. The combination of using this mirror for the inside the sphere tests along with careful

‘blanking’ procedures (for all tests) to properly account for other light losses resolved the discrepancies, and was then used in all final data acquisition in both the inside the sphere and outside the sphere configurations. Descriptions of those ‘blanking’ procedures are contained in Section 3.3.

33 3.2.2 External Sample Mounting: Normal Incidence Hemispherical Measurements

Normal incidence hemispherical measurements were made for both the transmittance and reflectance by mounting the samples outside the sphere, at either the entrance port or at the exit port. For the hemispherical transmittance measurements, the sample was mounted just outside the entrance port, while the reflectance port was covered with a flat black plate (Figure 8). In this configuration, some portion of the incoming light beam

Transmittance Mode Reflectance Mode

Figure 8: Schematic layout of integrating sphere in standard configuration, used to make normal incidence hemispherical measurements. Note that the turning mirror was used in both the transmittance and reflectance measurements for the outside the sphere configuration. was transmitted through the sample, while the rest is either absorbed by the sample or reflected away (outside the sphere). The light that was transmitted through the sample was then reflected off of the turning mirror onto an inner portion of the sphere, to prevent any direct reflection back onto the sample. This light would then make multiple bounces off of the interior of the sphere, eventually finding its way to the detector (some of the light undoubtedly impinged on the back side of the sample, which would then either be transmitted back through the sample, absorbed by the sample, or reflected off of the

34 sample; this is accounted for through a procedure referred to the substitution method of

‘sample blanking’, described in Section 3.3 ).

For reflectance measurements, the sample was installed in the exit port, mounted on an optically black plate (the black plate prevents any light which is transmitted through the sample from being reflected and re-transmitted back through the sample). The light was directed onto the sample using the turning mirror (Figure 8), with the light reflected off of the sample being internally reflected in the sphere, and eventually captured by the detector. Similar to the transmittance case, some light was lost due to either multiple reflections off of the sample, or due to losses back through the entrance port. These factors were accounted for with the ‘sample blanking’ procedures.

3.2.3 External Sample Mounting: ‘Forward Scattered’ Measurements

A perturbation of this set up was performed which allowed estimation of the angular extent to which a normal incidence beam is deflected when it is transmitted through a sample. This was done by changing the collection angle for the light that was transmitted from the sample. While the collection angle was πsteradians (full hemispherical) when the sample was mounted directly at the entrance/exit port, this collection angle was reduced by simply mounting the samples a distance away from the entrance port. Since the port had a fixed diameter, moving the sample away would reduce the amount of light captured, as the rest would effectively be lost outside the sphere. This approach was used

35 in normal incidence measurements (outside the sphere only) to give some indication of

the degree to which light was scattered off-axis.

To measure this ‘forward scattered transmittance’, the samples were mounted at distances

of 0.5, 1.0, 1.5 and 2.9 cm from the entrance port.The samples were mounted away from

the port using spacer rings of appropriate thickness, as illustrated schematically in Figure

9 and pictured in Figure 10. These rings were painted black (the black paint prevented

any light from the sample from being reflected into the sphere off the inside of the spacer

rings). This arrangement caused some of the light which was transmitted through the

sample but scattered at severe angles to fall outside of the collection angle of the port.

Figure 9: Schematic layout of integrating sphere when used to determine the ‘forward scattered’ transmittance. The angular extent of the scattering is measured by changing the collection angle from the sample to sphere; by increasing the distance from the sample to the aperture, the collection angle is reduced. This was accomplished by mounting the sample on ‘spacer rings’, which provided separation between the sample and the aperture.

36 Figure 10: Integrating sphere with spacer ring on entrance port with no sample (left), and with sample installed (right). This configuration was used to estimate how much light was transmitted through the sample, but scattered off-axis (termed ‘forward scatter’).

3.2.4 Internal Sample Mounting: Normal and Angular Incidence Measurements

Another configuration was developed to allow the hemispherical transmittance and reflectance to be measured at different incident angles. For this method, samples were mounted on custom sample holders that were placed inside the sphere by replacing the cover of the viewing port with a modified cover that provided a mounting point for the sample holders. The turning mirror (illustrated in Figure 8) was removed to allow the insertion of the custom sample holders as shown in Figure 11 (the mounting point for the turning mirror was used to mount the previously described ‘wedge-mirror’, which prevented any reflections from the back wall to be directly reflected back onto the sample, directly onto the detector, or directly out the entrance port). This arrangement allowed the samples to be mounted at different angles relative to the average angle of the

37 incoming beam*, and enabled the determination of the angular dependence of the radiative properties. This configuration (shown in Figure 12) was used extensively to acquire the majority of the data in this study.

Figure 11: Custom sample holders for inside the sphere tests. The solid sample holders (top row) were used to measure reflectance only, while the holders in the bottom row allowed measurement of both reflected and transmitted light.

Unlike the previous arrangement, this configuration does not allow the transmission from the sample to be measured independently of the reflectance. Instead, each angled data set was acquired first with the sample mounted on a solid sample holder that had a black surface. This allowed a direct measurement of the sample’s hemispherical reflectance at the given (average) incidence angle (as in the original configuration, any light transmitted through the sample would be absorbed by the black surface, rather than being reflected

* The incoming beam is not collimated, but converges at an angle of about 7 degrees from an initial diameter of 44.5 mm down to a ‘waist’ of 7 mm in diameter at its tightest focus, after which it diverges again at a similar angle. When averaged across the diameter of the beam, the angle of the beam is normal to the plane of the entrance port of the sphere. The waist diameter at the sample plane was dependent on which angle was being tested, since the non-normal incidence holders moved the samples further back in the path, and presented a different projected beam onto the sample. The waist diameter at the normal incidence sample plane for the inside the sphere tests was approximately 8 mm.

38 back and re-transmitted through the sample). An additional spectrum was acquired with the sample mounted on a holder with a large hole behind the sample, so that any transmitted light could pass through the sample. This spectrum was then a combination of light that was transmitted and light that was reflected. Subtraction of the reflection- only spectrum allowed determination of the transmittance, and applying conservation of energy and Kirchoff’s Law allowed calculation of both the absorptance and emittance at the given angle.

Transmittance + Reflectance Reflectance Only Mode Mode Figure 12: Schematic representation of sphere showing angled sample holder mounted inside sphere. This was the general configuration for most of the tests in this study.

39 3.3 ‘Sample Blanking’: Accounting for Light Losses, Detector & Light Source

Performance

A crucial step in the use of an FTIR instrument in typical spectroscopy applications (with or without an integrating sphere) is appropriate ‘sample blanking’. The purpose of this

‘blank’ sample is to acquire a background data set with no sample data in it, which provides a standard to ratio the sample data against (this ratio is required to present the data in the non-dimensional form of transmittance, etc., since the spectrometer itself essentially measures power as a function of wavenumber). If done properly, this procedure accounts for variations in the light source, detector performance, and all light losses. A sample ‘blank’ is produced by acquiring a set of data without a sample, but with the instrument and geometrical configuration in (theoretically) the identical configuration. The difficulty of acquiring an appropriate background (or ‘blank’) is that the presence of the sample itself constitutes a geometrical change to the system, which means that a blank taken without a sample in place does not constitute a proper blank.

Special methods (termed ‘substitution methods’) were used to incorporate the presence of the sample in the blank, without adding the sample’s data signature to the blank. The sample blanking procedures were repeated for each test with different samples, since the amount of light reflected off of a sample on a secondary reflection would be different, depending on the degree of pyrolysis of the sample.

These procedures account for losses and variations that differ somewhat between the outside and inside the sphere configurations. For the outside the sphere configuration,

40 the substitution method accounts for secondary reflections off of the back of the sample, as well as light transmitted back through the sample and lost. With the inside the sphere configuration, the substitution accounts for secondary bounces off of the sample, the presence of the sample holders, and losses through the entrance port.

3.3.1 Substitution Method for Outside the Sphere Configuration

Transmittance Configuration

The outside the sphere measurements required two separate ‘sample blanking’ procedures, one each for the transmittance and reflectance measurements. For the transmittance configuration (in which the sample was mounted externally, directly at the entrance port to the sphere), the differences specific to that configuration involve light that is lost by re-transmission back through the sample (after reflection off an interior wall of the sphere), and light that is reflected off of the back side of the sample back into the sphere.

To account for this, a background spectrum was acquired with a sample covering a black plate in the reflectance port in the bottom of the sphere, but with the turning mirror in the reference mode (i.e., with the light directed off of a interior wall of the sphere), not the reflectance mode. This is intended to “substitute” for both the loss of light that is retransmitted through the sample (and out the entrance port), and for the reflections occurring off the back of the sample at the entrance port when the actual data spectrum is

41 taken. By doing this, both the internal reflections off of the back of the sample and the losses through the entrance port are accounted for properly. This effectively allows a

‘substitution’ of losses from one port (the entrance port) during the background spectrum for the losses at the other port (the reflectance port) during the actual data acquisition, illustrating the term “substitution method”: one set of losses/inaccuracies in the blanking procedure (reflection off of the sample in the exit port, and complete loss through the entrance port) are ‘substituted’ for a similar set of losses/inaccuracies in the data spectrum (reflection off of the sample in the entrance port, and complete loss through the exit port).

For this substitution to be strictly valid, the areas of the entrance and exit ports would need to be identical. In the present case, the differences in those diameters of those ports

(entrance port diameter of 16.3 mm, exit port diameter of 19 mm) cause a difference of about 26% in area. However, initial testing showed that the ‘substitution’ method provided results that were about 5% more accurate than that obtained by simply acquiring a blank with no sample in place (even without substitution, ‘blanking’ is required to account for spectral variations in both the light source and the detector). Since the substitution method itself is a relatively small correction, than small differences in the small corrections amount to essentially very small errors present in the data.

42 Reflectance Configuration

The sample ‘blanking’ procedure for the outside the sphere reflectance configuration again utilizes a sample placed on a black plate mounted in the exit port of the sphere.

Similar to the transmittance configuration, the turning mirror, is used to aim the beam onto an interior portion of the sphere, causing light to indirectly fall onto the sample in much the same way that secondary reflections (off of the sample) could be reflected from the sample onto the sphere and back onto the sample during the collection of a data spectrum. For the actual data spectrum, the turning mirror is then positioned to aim the beam directly onto the sample, to perform the reflection measurement. The substitution in this configuration is that losses due to sample absorption after initial sample reflections in the data spectrum are substituted for losses by absorption from reflections onto the sample in the ‘blank’ spectrum. There is no error due to differences in port size for this case, since the sample is mounted on the same port for both the data spectrum and the

‘blank’.

Forward-Scatter Measurements

Blanking procedures for the forward scatter tests (in which the samples were mounted at specified distances from the ports by means of a series of spacer rings) were carried in similar fashion to those previously described, with the exception that the spacer rings were also installed for the sample ‘blank’ tests, to provide as similar geometry as possible for the substitutions.

43 3.3.2 Substitution Method for Inside the Sphere Measurements

The blanking procedures for the inside the sphere tests were performed similarly for both the reflection-only tests and the combination reflection/transmission tests, since the sample was mounted in the same geometric position for each test (described in Section

3.3.3). The ‘wedge-mirror’ was used for all inside the sphere tests, i.e., both data tests as well as ‘blank’ tests.

The combination reflection/transmission sample holder was used to acquire sample blanks for both the reflection-only and the combination reflection/transmission configurations. This allowed any stray reflections off of the edges of the sample holder to be accounted for, but also allowed light to pass through the hole, and be directed (off of the wedge mirror) around the sphere, similar to how light that was either reflected or transmitted off of a sample would be. For this blank, the sample was placed on a black optical plate, mounted in the exit port, and a smaller aperture was also used to stop down that port, making it similar in size to the aperture used on the entrance port for this configuration. To acquire actual sample data, the sample was simply removed from the black plate, and mounted on the appropriate angled sample holder. The black plate was then placed back in the exit port, and the data spectrum was acquired. This configuration provided the best substitution for the secondary reflections off of the sample, and accounted (as accurately as possible) for the presence of the sample holder. The validity of the inside the sphere configuration was determined by comparing the normal incidence

44 data for the inside configuration with that of the outside the sphere configuration

(discussed in Section 4.1).

3.4 Angled Sample Holders

Custom-made sample holders were used to position the samples at pre-determined angles relative to the incoming light beam for the angular tests within the integrating sphere.

For this work, the incident angle is defined as the angle relative to normal impingement on the sample. This convention was chosen since the setup where the incoming light beam is perpendicular to the sample (‘normal’ incidence) is considered the baseline configuration, and is then called 0o incidence angle. Small angular variations from this would then correspond to small angles (i.e., 15o deviation from normal incidence is considered a 15o angle).

Sample holders were fabricated to allow samples to be mounted at angles of 0o, 15o, 30o,

45o and 60o relative to the average incoming beam (Figure 11). The unique shape of some of the sample holders was needed to allow placement of the sample in the appropriate position in the sphere, without mechanically interfering with the light baffles.

The sample holders were made of aluminum and were bead blasted, to provide diffuse reflections off of the structure of the sample holder. Two types of sample holders were used for each angular measurement. These holders were configured with a sample mounting area that had either a solid region behind the sample, or a hole that was larger than the light beam. The hole diameter was 14 mm for all sample holders, except for the

45 60o holder, which had a diameter of 21 mm. While the smaller hole was sufficient to allow the light beam to pass completely through for all angles up to 45o, the severe incidence angle of the 60o holder dictated that a larger hole be used.

Samples were mounted on either the solid sample holder with the flat black surface, or on the sample holder with the hole in the mounting area. Though care was taken to use an aperture on the entrance port that was small enough to reduce the beam size to less than the sample size, the front surfaces (the surface facing the entrance port) of all sample holders were painted black to insure that any small fraction of light that would unintentionally strike the sample holder would be absorbed, rather than reflected into the sphere. Small pieces of tape were used to mount the sample to the holders, but care was taken to insure that the tape was not in the path of the incoming beam, to prevent co- mingling of the spectral signature of the tape with that of the sample. This allowed measurement of reflection only (with the sample mounted on the flat black region), or measurement of the combined reflection and transmission (with the sample mounted over the hole on the holder).

46 3.5 Data Reduction

3.5.1 Basic Data Reduction

As previously described, data was collected in several configurations. The first configuration allowed measurement of the hemispherical spectral properties at normal incidence angles for each of the charred samples. When data was acquired with the sample mounted at the entrance and reflection apertures of the sphere, the collection angle for transmitted and reflected light was large. This arrangement allowed the normal- incidence, hemispherical spectral transmittance and reflectance to be directly measured.

From these measurements, the data was reduced to yield values for the hemispherical absorptance ‘()’ (where stands for wavelength), the hemispherical emittance (), the hemispherical reflectance ‘()’, and hemispherical transmittance ‘()’, all spectrally resolved and at normal incidence. The parameters (), (), and () are related through conservation of energy, shown in Equation 2:

() + () + () = 1 Equation 2

where is substituted for under the assumptions relevant to Kirchoff’s Law. The direct measurements of the hemispherical reflectance and the hemispherical transmittance

47 (each at normal incidence) allowed the hemispherical emittance to be immediately calculated.

Measurement of the transmitted light when the sample was mounted a distance away from the sphere allowed some estimation of the angular extent of the forward scattering.

This was done by subtracting the signal measured with the sample away from the entrance from that acquired with the sample mounted at the entrance. The difference between those two quantities was the light that was lost (i.e., not collected by the sphere) due to changing the collection cone angle. That quantity was termed the ‘forward scattering’ (denoted as fs(λ)), and could be described as the normal-incidence, angular transmittance. A similar arrangement was also used in which the sample was mounted a distance from the reflectance port, giving the normal-incidence, angular reflectance

(termed ‘back scattering’, denoted bs(λ)). For these measurements, the difference between the measured value with the sample at the aperture and the value obtained with the sample some distance away from the port is the light lost due only to the changing collection angle. Equation 3 shows the expression for the forward scattering:

()at entrance port - ()away from port = fs(λ) Equation 3

where fs(λ)θis the normal-incidence spectral transmittance (also referred to as ‘forward scattering’), integrated at scattering angles from 180o (full cone angle) to the angle θ

(indicated in the subscript).

48 Equation 4 describes the normal-incidence ‘back scattering’ (i.e., reflectance):

()at entrance port - () away from port = bs(λ) Equation 4

where bs(λ)θis the normal incidence spectral reflectance (also referred to as ‘back scattering’), integrated at scattering angles from 180o (full cone angle) to the angle θ

(indicated in the subscript).

The other configuration allowed measurement of the hemispherical, spectral properties at different incident angles. This required mounting the samples at the desired angle

(relative to the incoming light beam) inside the integrating sphere, on the previously described custom sample holders.

This setup required that data be acquired with the sample mounted in two different ways for each angular measurement. Data acquired with the sample mounted on a solid, optically black sample holder provided a direct measurement of hemispherical reflectance at the given incidence angle, similar to that from the normal incidence configuration.

Data was also taken with the sample mounted on a sample holder that had a large hole directly behind the sample, allowing both reflected and transmitted light to be measured

(measurement designated ‘M1’ below). The transmittance was determined by subtracting the reflectance (as measured with the sample on the flat black holder, measurement designated ‘M2’ below) from the ‘transmittance plus reflectance’ measurement. The absorptance and emittance were determined by applying conservation of energy and

49 Kirchoff’s Law, as in the normal incidence configuration. Equations 5-8 represent these relationships:

M1= τ(λ) + ρ(λ) Equation 5

M2 = ρ(λ) Equation 6

M1 - M2 = τ(λ) Equation 7

1 - ρ(λ) - τ(λ) = ()

or Equation 8

1 – M1 = ()

3.5.2 Band-Integrated Values

Determination of band-integrated radiative properties requires that the spectrally resolved property values be applied to a Plank blackbody function at a given temperature. This gives a spectrally resolved flux, which can then be integrated over the desired spectral range and compared to the flux from a blackbody at the same temperature. This is then carried out using Plank functions at a variety of temperatures, to give the temperature dependence of the given sample. These operations were carried out using spreadsheets to perform both the Plank function calculations and the spectral integrations.

Samples at different levels of pyrolysis were then selected to represent the spectral behavior of a burning sample at different stages of the combustion process. Estimation was made of what temperatures would likely produce samples similar to the selected test

50 samples, based on results of a current generation numerical model. The temperature dependent band integrated dataset was then developed by performing the integrations using temperature values appropriate for each sample.

3.5.3 Comparison of Surface Emittance and Absorptance from a Flame

The heat transfer between the surface and a flame at an elevated temperature was studied by examining the integrated emissions from the (spectral) surface at an assumed temperature, and comparing that with the energy absorbed by the same surface when exposed to the spectral emissions of a representative flame at a higher temperature. The band-integrated emission from the surface was calculated as previously described.

Calculation of the energy absorbed by the surface required knowledge of the spectral emission of the flame. This was accomplished by assuming a layer of heated gas of uniform temperature and thickness, with given species concentrations. The temperature was selected as an average flame temperature determined by a numerical model under a given condition5. The thickness of the gas layer (optical pathlength) was chosen to be 1 cm, assumed to be representative of a typical optical path in a flame. Species concentrations were chosen to be typical values computed by the model.

The selected values of temperature, path length and concentrations were then used to calculate the spectral response of the gas mixture, using the HITEMP data base. This spectral response was then applied to the Plank function (at the flame’s assumed

51 temperature) to give a spectral radiant flux. This flux was then multiplied (spectrally) by the absorptance of the surface, and integrated across the entire spectrum (within the limits of the measured spectral data). This allowed comparison of the broadband emittance of the surface with its absorptance, when in the presence of the ‘assumed’ flame.

52 4.0 Results & Discussion

4.1 Comparison of Inside vs. Outside the Integrating Sphere Tests

Measurements were made using both the ‘inside’ and ‘outside’ the integrating sphere configurations for several reasons. The angular dependence (with respect to the angle of the incoming light beam) could only be measured using the inside the sphere technique, yet the outside the sphere tests allowed some estimation of the degree to which the sample could deflect transmitted light off-axis. Since both techniques were employed, the equivalence of the tests (for normal incidence only) needed to be established. Greater credibility could be placed in the measurements from both techniques if they could be shown to produce similar results for a similar configuration. Since the primary method of data collection employed the inside the sphere configuration, a comparison of the two techniques is presented first to demonstrate their equivalency.

Figure 13 shows the results for the hemispherical transmittance at normal incidence for both the inside and outside configurations. This plot shows virtually identical results across most of the spectral domain, with differences in limited regions never exceeding

4%. While these small differences in transmittance suggest that very small differences may exist between the techniques, the similar results (within experimental uncertainty) indicate that equivalence is established.

53 Comparison of Inside vs Outside Sphere Methods

100% Virgin KimWipes Normal Incidence Angle Wedge Mirror & Sub. Method (Both)

e 75% c n a

t Outside the sphere t i Inside the sphere

m 50% s n a r

T 25%

0% 0 5 10 15 20 Wavelength (microns)

Figure 13: Transmittance of virgin KimWipes® using both inside the sphere and outside the sphere methods.

4.2 Data Sample Set

Samples for this study were generated by heat treating virgin KimWipes® in a constant temperature furnace for varying time periods. The choice of furnace temperatures and heat treatment times was driven by a balance between the need to replicate conditions that could be expected in a true combustion situation with the practical aspects of producing such samples in a controlled fashion, and in sufficient quantities. Guidelines for the temperatures at which significant pyrolysis effects would occur were found by using a numerical model to examine the calculated area density as a function of temperature in a steady state, concurrent flow configuration, for a variety of

54 conditions21,23 (Figure 14)*. This data shows that for temperatures below 500 K, very little mass loss occurs. However, by the time the surface reaches 700 K, most (or all, depending on the conditions) of the mass is consumed.

Area Density vs Temperature: Concurrent Flow

10 cm/sec, 21% O2 (Tolejko data) 0.0025 2 cm/sec, 21% O2 (Feier data) 5 cm/se, 15% O2 (Feier data) 15 cm/sec, 15% O2 (Feier data) ) 2 0.0020 m c / g ( 0.0015 y t i s n

e 0.0010 D

a e r 0.0005 A

0.0000 400 500 600 700 800 Temperature (K)

Figure 14: Numerical calculations showing area density as a function of surface temperature for concurrent flow flame spread. Note that the 10 cm/sec, 21% O2 data was calculated using an initial area density of 2 mg/cm2. While this changes the magnitude of the curve slightly, the behavior of the area density with respect to temperature is essentially the same as that of the other data. (Numerical data courtesy of Ioan Feier23 and Kevin Tolejko24).

Initial testing showed that samples could be generated in furnace temperatures up to approximately 673 K, though at that temperature the duration of heat treatment required to achieve loss of 50% of the original mass was only 8 seconds. Testing also showed that below 600 K, the heat treatment times needed to achieve mass loss levels of 50% reached

* Note that two oxygen conditions (21% and 15%) were used in the plotted numerical data. However, the 2 initial area density used in the 21% O2, 10 cm/sec calculation was 2 mg/cm , which is 10% higher than the 2 actual value of 1.8 mg/cm , which was used in the 18%O2 data. Still, the shape of the curves are very similar, with the 21% O2 data being consumed at a temperature similar to that of the 18% O2 tests. This suggests that the area density (as a function of temperature) is not particularly sensitive to the ambient O2 concentration, therefore, the 15% O2 data (which was available at the proper initial area density) is representative of similar data at other O2 concentrations.

55 3 minutes, so this was deemed the lowest practical temperature to use. Based on this initial information, heat treatment temperatures of 598 K, 623 K, 648 K and 673 K were selected. Heat treatment times varied from as little as 3 seconds (for minimally charred samples at 673 K) to as great as 180 seconds (heavily charred samples at 598 K). While a considerable sample set was created, practical limitations dictated that only a subset is used for spectroscopic analysis. The remaining samples were used as backups, when a primary sample was damaged during handling. This large group of extra samples was also used in determining the activation energy and pre-exponential factor used in the numerical model, discussed in Section 4.6. The overall data set is shown as both black and colored markers in Figure 15, overlaid on the calculated traces of area density vs. temperature (the colored markers represent a subset of data, explained in Section 4.2.1).

Area Density vs Temperature: Concurrent Flow 0.0025 2 cm/sec, 15%O2 5 cm/sec, 15%O2 15 cm/sec, 15%O2 )

2 0.0020 m c / g ( 0.0015 y t i s n e 0.0010 D

a e r

A 0.0005

0.0000 400 500 600 700 800 Temperature (K)

Figure 15: Area density as a function of surface temperature for several different concurrent flow combustion cases, as determined by numerical model. Dots represent experimental data points at the indicated temperature and area density. Black dots show overall data set, while colored dots show points used for heat treatment comparison. (Numerical data courtesy of Ioan Feier23).

56 4.2.1 Determination of Data Subset to be used for Spectroscopic Analysis

The overall sample set of this study is comprised of samples treated at four different temperatures for differing times. The large combination of heating temperatures and treatment times presents the problem of determining the conditions in which samples that were produced would be representative of the spectral behavior of a fuel sample undergoing the combustion process. These samples also appeared qualitatively similar, in visual appearance, further complicating the decision of which samples were most representative of those that would be observed in a true combustion case. Figure 16 shows the series of samples acquired at 623 K (with different heat treatment times), which are representative of the samples produced at other temperatures in this study.

10 sec 30 sec 40 sec 50 sec 90 sec 2 1.79 mg/cm2 1.32 mg/cm2 1.15 mg/cm2 0.84 mg/cm2 0.46 mg/cm

4 cm

Figure 16: Series of KimWipes® samples produced at heat- treatment temperature of 623 K for different times.

57 Examination of the numerical data21,23 showing area density as a function of temperature demonstrates a monotonic decrease in area density as temperature increases, after the temperature reaches about 550 K. Figure 15 shows the overall data set overlaid on the calculated area density data plot. The five different colored sets of data points denote samples of approximately similar area densities achieved at different temperatures, spanning most of the range of sample area densities that were achievable, while the black dots represent the remainder of the data set. The normal incidence absorptance data from each of these sample sets were compared to examine the effect of heating history on the radiative properties, as the absorptance data is indicative of effects seen in both reflectance and transmittance. Comparison of samples within each given set, as well as overall comparison between sets gives an indication of the role of area density in the behavior of the spectral properties. Since area density is strongly dependent on the temperature of the sample (i.e., area density decreases as the sample is heated), the dependency of the spectral values on area density can capture some of the thermal effects on the spectral property values. Further, comparisons of differences or similarities between these groups of samples can be used to help determine which of the sample conditions are the most appropriate to consider representative of a combusting sample.

A parametric examination of the angular data at each angle for each case is not instructive, as qualitatively similar angular trends are seen in each case. Both normal incidence and angular data from several of the comparison groups will be discussed to demonstrate this similarity.

58 4.2.3 Comparisons by Area Density: Normal Incidence

Case I: Lightly Charred Samples

The first comparison case uses lightly charred samples created at each of the four test temperatures. These data points have an average area density (AD) of 1.53* mg/cm2 (all similar within 8% of each other), and are indicated by blue markers in Figure 15. Table 1 shows the temperature and heat treatment time for each sample, as well as its area density.

Furnace Heat Treatment Area Density Temperature (K) Time (sec) (mg/cm2) 598 60 1.51 623 10 1.60 648 5 1.52 673 3 1.48 Average Area Density: 1.53 Table 1: Heat treatment temperature, treatment time, and area density for Case I samples.

Figure 17 shows the normal incidence absorptance for this sample set, with that of virgin

KimWipes® also plotted for comparison. The average area density of these samples is approximately 17% less than that of virgin KimWipes®, yet the spectral properties show virtually no changes in any spectral region except at 5.8 microns (the carbonyl band, discussed in Section 4.4.7). Aside from that region, the variation at any wavelength between the virgin sample and any in this set is 4% or less.

* Experimental uncertainty on all area density measurements is +/- 0.07 mg/cm2. Details available in Appendix IV.

59 AbsorptanceAbsorptance of Lightly of Charred Charred KimWipes KimWipes Inside Sphere 100% Normal Incidence Similar AD's with different heating histories

e 75% c n a t p

r 50% 2 o 598598 K, , 60 60 sec, sec, 0.00151 1.51 mg/cm g/cm2 s 2

b 623623 K, K, 10 sec, 1.60 0.00160 mg/cm g/cm2 A 25% 648648 K, K, 5 sec, 1.52 0.00152 mg/cm g/cm22 2 ~7% variation in area density 673673 K, K, 3 3 sec, sec, 1.48 0.00148 mg/cm g/cm2 ~4% variation in absorptance VirginVirgin KimWipes, KimWipes, 1.850.00185 mg/cm g/cm22 0% 0 5 10 15 20 25 Wavelength (microns)

Figure 17: Absorptance of lightly charred KimWipes®, Case I samples, normal incidence.

Case II: Moderately Charred Samples

This data set, shown in pink markers in Figure 15, also compares data acquired at different treatment times from all four of the tested temperatures. These samples have an average area density of 1.35 mg/cm2 and are all within 4% of each other, but differ (on average) from the virgin material by 27%. Table 2 lists the relevant heat treatment

Furnace Heat Treatment Area Density Temperature (K) Time (sec) (mg/cm2) 598 120 1.36 623 30 1.38 648 10 1.34 673 5 1.33 Average Area Density: 1.35

Table 2: Heat treatment temperature, treatment time, and area density for Case II samples.

60 information and area density for each sample.

Figure 18 shows the absorptance for these samples along with that of the virgin material.

Similar to Case I, this group of samples shows little variation in the absorptance for most of the spectral range, with a significant exception being the carbonyl band (5.8 microns).

While the data for wavelengths longer than 12 microns shows some small variations, each of the data traces is within 5% of all others within the group.

AbsorptanceAbsorptance of Moderately of Charred Charred KimWipes KimWipes Inside Sphere Similar AD's with 100% different heating histories

e 75% c n a t p

r 50% o 2 s 598 K, 120 120 sec, sec, 0.001361.36 mg/cm g/cm2 b 623 K, 30 30 sec, sec, 0.001381.38 mg/cm g/cm22 A 25% 648 K, 10 10 sec, sec, 0.00134 1.34 mg/cm g/cm22 673 K, 5 5 sec, sec, 0.00133 1.33 mg/cm g/cm22 Virgin KimWipes, KimWipes, 0.00185 1.85 mg/cm g/cm22 0% 0 5 10 15 20 25 Wavelength (microns)

Figure 18: Absorptance of moderately charred KimWipes®, Case II samples, normal incidence.

However, this data set does begin to show noticeable variation from the virgin absorptance. This is particularly noticeable at longer wavelengths, with the average absorptance for the sample group falling about 9% less than that of the virgin sample for wavelengths longer than 12 microns.

61 Case III: Heavily Charred Samples

The next comparison set is comprised of samples taken at 623, 648 and 673 K, shown in

Figure 15 with green markers. This set averages 1.16 mg/cm2 with a sample to sample variation in area density of 5%, but is 37% lower in area density than virgin KimWipes®.

Table 3 lists the heat treatment conditions and area density of each sample.

Furnace Heat Treatment Area Density Temperature (K) Time (sec) (mg/cm2) 623 40 1.13 648 15 1.15 673 7 1.19 Average Area Density: 1.16 Table 3: Heat treatment temperature, treatment time, and area density for Case III samples.

The normal incidence absorptance data for these samples (Figure 19) shows similar behavior to the Case II samples, with agreement (within the set) to 2% up to about 12 microns, after which there is a slight divergence of up to 6%.

The absorptance of virgin KimWipes® is again plotted in red, to allow comparison to the virgin property. This shows a reduction (in the charred samples) of up to 9% for most spectral regions below 12 microns, after which the difference increases to as much as

15%.

62 AbsorptanceAbsorptance of Heavily of Charred Charred KimWipes KimWipes Inside Sphere Inside Sphere Similar AD's with Normal Incidence 100% Normal Incidence different heating histories

e 75% c n a t p

r 50% o s 623623 K, 40 40 sec, sec, 1.31 0.00131 mg/cm g/cm22 b 2 A 648648 K, 15 15 sec, sec, 1.15 0.00115 mg/cm g/cm2 25% 2 ~5% variation in area density 673673 K, 7 7 sec, sec, 0.001191.19 mg/cm g/cm2 2 ~6% variation in absorptance Virgin KimWipes, 1.850.00185 mg/cm g/cm2 0% 0 5 10 15 20 25 Wavelength (microns)

Figure 19: Absorptance of heavily charred KimWipes®, Case III samples, normal incidence.

Case IV: Very Heavily Charred Samples

The comparison set for cases IV and V include only two samples for each case, as only the 623 K and 673 K temperatures were used to create samples that were pyrolyzed to such an extent. The points for Case IV are seen as red markers in Figure 15, with Table 4 showing the heat treatment data and area densities. The average area density of these samples (0.78 mg/cm2) is 58% of that of the virgin material.

Furnace Heat Treatment Area Density Temperature (K) Time (sec) (mg/cm2) 623 70 0.80 673 12 0.73 Average Area Density: 0.78 Table 4: Heat treatment temperature, treatment time, and area density for Case IV samples.

63 The spectral absorptance data for these samples is shown in Figure 20, along with that of virgin KimWipes®. The data for the two Case IV samples shows very good agreement through most of the spectral range, with a maximum of 6% variation occurring between 7 to 8.5 microns, and again from 10.5 to 14 microns.

AbsorptanceAbsorptance of Very of Heavily Charred Charred KimWipes KimWipes Inside Sphere 100% ~ 5%deviation in A.D.

75% e c n a t p

r 50% o s b

A 2 25% 623 K, 70 70 sec, sec, 0.000800.80 mg/cm g/cm2 2 673 K, 12 12 sec, sec, 0.000750.75 mg/cm g/cm2 Virgin KimWipes, KimWipes, 0.00185 1.85 mg/cm g/cm22 0% 0 5 10 15 20 25 Wavelength (microns)

Figure 20: Absorptance of very heavily charred KimWipes®, Case IV samples, normal incidence.

These samples show a reduction in absorptance of 12-15% for wavelengths shorter than

5.1 microns, compared to that of virgin KimWipes®. From 5.1 to 6 microns, the previously discussed carbonyl band is noted, and for longer wavelengths, the difference between the virgin and charred samples grows to between 20-30%.

64 Case V: Severely Charred Samples

The final comparison set also was created at temperatures of 350 C and 400 C. These points are represented as light green color markers in Figure 15. The average area density for these cases is 0.40 mg/cm2, which is less than 22% of the original (virgin material) area density. Table 5 shows the heat treatment times and area densities of these two samples.

Furnace Heat Treatment Area Density Temperature (K) Time (sec) (mg/cm2) 623 90 0.40 673 16 0.40 Average Area Density: 0.40 Table 5: Heat treatment temperature, treatment time, and area density for Case V samples.

The normal incidence spectral absorptance data for these samples is shown in Figure 21.

The agreement in the spectral data for these two samples appears to be slightly less than that of the previous cases, with a difference of up to 8% between the samples seen for wavelengths longer than 8 microns. However, the spectral trends between these samples, which are considerably different from those of the previous groups, are consistent with each other. Moreover, the fixed uncertainty in the area density measurement

(+/- 0.07 mg/cm2, see Appendix IV) is a larger fraction of the total measurement for the most severely charred samples. This uncertainty in the area density suggests that the differences observed in the spectral data may be attributable to the uncertainty in the actual area density of the two samples, though other factors such as small differences in sample mounting, spatial non-uniformity, etc, could also play a role.

65 AbsorptanceAbsorptance of Severely of Charred Charre KimWipesd KimWipes Inside Sphere 100% ~ 2% deviation in A.D.

75% e c n a t 623623 K, K, 90 sesec,c, 0.40 0.00040 mg/cm g/cm22 p 2

r 50% 673673 K, K, 16 sec, 0.40 0.00040 mg/cm g/cm2 o 2 s VirginVirgin KimWipes, KimWipes, 1.85 0.00185 mg/cm g/cm2 b

A 25%

0% 0 5 10 15 20 25 Wavelength (microns) Figure 21: Absorptance of severely charred KimWipes®, Case V samples, normal incidence.

4.2.4 Comparisons by Area Density: Angular Data

The samples from comparison Case III at 45 degree incidence and from Case V at 30 degree incidence were also used to evaluate whether samples of similar area densities from different heating paths exhibit similar angular dependency. The possibility of the angular dependence of the spectral properties also being dependent on the thermal history of the sample was explored by examining data taken at the two different incidence angles and two different area densities. These groups were selected for discussion because they are representative of significant pyrolytic effects with samples from different thermal histories, with data acquired at different incidence angles.

66 Case III Samples, 45 Degree Incidence

Figure 22 shows the spectral absorptance of the Case III samples at 45 degree incidence.

As previously discussed, these samples had similar area densities to within 5%, though all were generated at different heat treatment temperatures and times. Like the normal incidence data for this comparison group (Figure 19), the spectral data from each of the different samples is virtually indistinguishable for wavelengths smaller than 11 microns, with a deviation of 6% or less at longer wavelengths.

Absorptance of Charred KimWipes o Inside Sphere, 45 Incidence Similar AD's with 100% different heating histories e

c 75% n a t p r

o 50% s

b 623623 K, K, 0.00113 1.13 mg/cm g/cm22 A 2 25% 648648 K, K, 0.00115 1.15 mg/cm g/cm2 ~5% deviation in AD 673 K, 1.19 mg/cm2 ~6% or less change in abs. 673 K, 0.00119 g/cm2 0% 0 5 10 15 20 25 Wavelength (microns)

Figure 22: Absorptance of charred KimWipes®, Case III samples, 45o incidence.

67 Case V Samples, 30 Degree Incidence

The spectral absorptance for the Case V samples at 30 degree incidence is shown in

Figure 23. As previously discussed, these samples are similar in area density to within

5%. The spectral data shows agreement to within 3% for wavelengths up to 7 microns, after which there is a mostly steady 5% difference in absorptance. While the spectral differences are small, it is noted that the sample which has a slightly greater area density

(0.80 vs. 0.75 mg/cm2) also exhibits the slightly greater spectral absorptance.

Absorptance of Charred KimWipes Inside Sphere, 30o Incidence 100% ~ 5% deviation in A.D.

2 75% 623623 K, K, 70 70 sec, sec, 0.00080 0.80 mg/cm g/cm2 e 673 K, 12 sec, 0.75 mg/cm2 c 673 K, 12 sec, 0.00075 g/cm2 n a t p

r 50% o s b

A 25%

0% 0 5 10 15 20 25 Wavelength (microns)

Figure 23: Absorptance of charred KimWipes®, Case V samples, 30o incidence.

Overall Comparison of Cases I-V

Figure 24 shows the normal incidence absorptance for each of the tests compared in

Cases I-V, color coded by group. The scatter within each case is a function not only of the uncertainty of the spectral data (+/- 5.8%) but also of the small variations (generally,

68 about 5%) in area density within each group. Since the samples within each group were created with different thermal histories (i.e., they were heat treated at different temperatures for different times), this plot shows the clear trend that the spectral values of absorptance are generally a function of area density, not thermal history, with the absorptance decreasing as the area density decreases. While some small spectral variations potentially may be related to the thermal history of the sample or other issues such reproducibility factors, the overall effects are seen regardless of the rate at which the sample was pyrolyzed.

Absorptance of Charred KimWipes Inside Sphere 100% Normal Incidence Similar AD's with different heating histories 75% e c n a t p

r 50% o s b 2

A CaseGroup I I(~1.55 (~ 0.00155 mg/cm g/cm2)) 25% 2 CaseGroup II II (~1.36 (~ 0.00136 mg/cm g/cm2)) CaseGroup III III (~1.15(~ 0.00115 mg/cm g/cm2)2) CaseGroup IV IV (~0.78 (~ 0.00078 mg/cm g/cm2)2) 0% 0 5 10 15 20 25 Wavelength (microns)

Figure 24: Absorptance of charred KimWipes® at normal incidence for comparison Cases I-V.

Similar trends where observed with regards to different incidence angles. The comparison of the Case III and Case V samples at two different incidence angles shows similar spectral trends at each angle.

69 The previously discussed comparisons of samples of similar area density from different heating histories shows that a correlation can be made between spectral behavior and sample area density, independent of the heating history. Therefore, any of the samples

(of approximately equal area density) can be used to represent that group. This finding has significant implications in numerical modeling efforts (which would use these results as property values), as the correlation of spectral data to area density alone is much simpler to implement than one that accounts for the sample’s heating history.

4.2.5 Area Density Effects on Virgin KW: Stacked Samples vs. AFP

For a substance in a gas or liquid phase, the absorption process is a function of pathlength through the given material and concentration of the material. For the solid material

(KimWipes®) used in this study, the combination of those two factors can be expressed as area density. Since the previous section showed that the spectral absorptance decreases as the area density decreases, a natural extension to the work is to verify that the absorptance increases if the area density increases.

One way to verify this is to spectroscopically examine stacked layers of KimWipes®.

While stacking layers of homogeneous materials (such as plates of glass) is not the same as merely increasing the thickness of a single layer, this limitation is not applicable to

KimWipes®, which are a loosely woven ‘mat’ of individual fibers. The surface reflections seen at each interface between layers of homogenous materials do not occur.

Instead, reflections happen at each fiber, which happens both internally to a single layer

70 and between layers. The stacked layers of KimWipes® then have comparatively little structural difference than one single layer of (hypothetically) thick KimWipes®, as opposed to discrete layers of homogenous material.

An additional question to answer is whether the nearly pure cellulose that composes

KimWipes® would give a similar spectral signature if it were processed in a different form, provided that the area densities were similar. This question can be addressed by examining the spectral signature of Ashless Filter Paper #4 (AFP), a filter paper manufactured by the Whatman Company for use as laboratory filters. Both KimWipes® and AFP are composed of greater than 99% cellulose, with less than 1% binder materials.

AFP has an area density of 8.56 mg/cm2 (full thickness), which is a factor of 4.6 times that of KimWipes®.

The different structural form of these two samples is seen in magnified images shown in

100 microns 100 microns

KimWipes (single sheet) Ashless Filter Paper (single sheet) 80X magnification 80X magnification Figure 25: Magnified images of virgin KimWipes® and virgin Ashless Filter Paper® (AFP).

71 Figure 25. These images show that the KimWipes® are composed of loose mats of longer fibers, while the AFP shows a more dense packing of smaller, finer fibers.

Figure 26 shows the spectral results of this comparison. This plot shows the spectral

Thickness Effects: Mutliple Sheets of KimWipes & AFP 100% Virgin KimWipes & Virgin AFP Data acquired using outside the sphere method

KimWipes: 1 sheet

e 75%

c KimWipes: 2 Sheets n

a KimWipes: 4 Sheets t t i 50% Ashless Filter Paper: 1 sheet m s n a r

T 25%

0% 0 5 10 15 20 25 Wavelength (microns)

Figure 26: Spectral transmittance of 1, 2, and 4 sheet layers of KimWipes®, as well as Ashless Filter Paper (AFP). The area density of 4 sheets of KimWipes® is comparable to that of AFP. The spectral transmittance of 4 sheets of KimWipes® is similar to that of AFP. transmittance of 1, 2 and 4 sheets of KimWipes®, as well as a single thickness of AFP®.

The transmittance for the 4 sheets of KimWipes® is similar to that of the AFP®, with differences of about 4% at wavelengths lower than 6 microns. Overall, the 4 layers of

KimWipes® show a slightly higher transmittance than AFP®, which is consistent with the fact that the composite area density of the 4-layer KimWipes® (7.39 mg/cm2) is a little less than that of AFP® (8.56 mg/cm2), even though the transmittance values are within the expected experimental uncertainty of each other.

This brief comparison of layered KimWipes® with Ashless Filter Paper® shows that the transmittance of these cellulosic fuels is proportional (inversely) with area density, in

72 ranges above and below that of virgin KimWipes®. Though the reflectance data was not acquired for layered KimWipes® (and therefore, the absorptance cannot be directly calculated), a strong inference can be made that absorptance is proportional to area density for this material, as well.

4.3 Final Dataset Used to Represent Spectral Behavior of KimWipes®

The results of the comparison of the spectral properties for similar area density from

Sample # Heat Treatment Heat Area Percentage of Temperature (K) Treatment Density Original Area Time (sec) (mg/cm2) Density 0 n/a n/a 1.85 100% 13 623 10 1.62 88% 72 598 120 1.25 68% 82 673 12 0.77 42% 29 623 90 0.40 21%

Table 6: Subset of samples used to represent spectral property data for burning KimWipes. different thermal histories showed the spectral behavior of the material is independent of thermal history, and is only a function of area density over the tested spectral domain

(small exceptions exist in limited spectral regions). This conclusion allows samples from any heat treatment regimen to be used to represent the spectral behavior of all samples of that area density.

73 This simplification allowed a sample set to be chosen from among those samples that survived the handling during testing long enough to provide data at each different angle, independent of what heat treatment temperature and time were used to create the sample.

The choice of the sample set was made by selecting samples that were approximately evenly spaced over the range of available area densities. This final sample set is shown in Table 6, showing heat treatment conditions and area density for each sample.

All heat-treated sample data for incidence angles of 0 degrees (normal incidence) through

45 degrees was acquired using the same sample, re-mounted on each of the different angled sample holders. However, the process of handling the relatively fragile sample multiple times usually caused tears, cracks or other loss of portions of the sample (for example, the small bit of tape used to hold the sample in place would tear off a portion when removed). Also, the opening in the 60 degree sample holder for the ‘τ + ρ’ measurement was larger than the others, so a fairly large sample was needed to cover the hole. Since the previously used samples (for the previous angular measurements) were typically heavily damaged by then, a sample from the same conditions (with similar area density) was used for the 60 degree measurements.

4.4 Spectral Radiative Properties

As previously described, a limited amount of data was acquired with the samples mounted outside the integrating sphere. Previous comparisons showed equivalency of

74 the two methods for normal incidence transmittance data. The outside the sphere configuration also allowed a limited evaluation of the scattering nature of the material, which was initially suspected due to the non-homogeneous, fibrous nature of this material. This scattering behavior carried implications for the nature of this experiment, demonstrating the need to use an integrating sphere to make radiative property measurements in such materials. This phenomenon also carries implications about what the limiting values of the radiative properties may be, as the incident angle is increased.

Accordingly, the scattering nature of the samples is examined prior to discussing the spectral and angular dependencies.

4.4.1 Normal Incidence Light that is Transmitted Off-Axis: ‘Forward Scattering’

A transmission test was performed with virgin KimWipes® samples mounted directly outside the entrance port to the sphere, and at distances of 0.5, 1.0, 1.5, and 2.9 cm from the entrance. The distance of 2.9 cm was the maximum distance that the sample could be mounted from the sphere, with the available FTIR bench. The difference in signal between the configuration in which the sample was mounted at some distance from the entrance and that measured with the sample mounted directly at the entrance to the sphere can be attributed to the difference in collection angle between the tests.

The collection angle is defined here as the total angle (twice the cone angle) from a point source which would be intercepted by the planar entrance port of the sphere. Although the incoming beam is known to have a measurable area, modeling it as a point source

75 serves as a first order approximation which serves to illustrate the angular extent of the forward scattering effect. The collection angle (full cone angle) for this geometry in this

Distance from Total collection entrance (cm) angle (degrees)

0 180o 0.5 84o 1 48o 1.5 33o 2.9 18o

Table 7: Estimated total collection angle at different sample mounting distances experiment ranges from 180 degrees (with the sample mounted directly at the sphere aperture) to 18 degrees. Table 7 shows the relation between the sample’s distance from the entrance to the sphere and the estimated collection angle.

Results for these tests are shown in Figure 27. This plot demonstrates that a significant fraction of the energy transmitted through the sample is re-directed in a generally

“forward” direction, but off axis from the incoming beam. Though this ‘forward scattering’ is spectrally dependent, several regions show that a significant fraction of the incoming energy is transmitted through the sample but deflected from the incoming axis.

This demonstrates the need to use an integrating sphere to properly capture all of the energy for the radiative property measurements, as a straight line measurement would erroneously conclude that much less energy actually passed through the sample. Since the determination of absorptance is indirect (it is calculated, using conservation of energy and measurements of transmitted energy and reflected energy), making the FTIR

76 Forward Scattered Transmittance of KimWipes Virgin KimWipes 100% Entrance to sphere (180 deg) 0.5 cm from entrance (84 deg) 1.0 cm from entrance (48 deg)

e 75%

c 1.5 cm from entrance (33 deg) n

a 2.9 cm from entrance (18 deg) t t i 50% m s n a r

T 25%

0% 0 5 10 15 20 25 Wavelength (microns)

Figure 27: Forward scattered transmittance of virgin KimWipes® that is captured by the integrating sphere. Samples were mounted at different distances from the sphere entrance, yielding less measured transmittance as the distance increased. measurements without an integrating sphere would fail to account for this ‘forward scattered’ transmitted energy, and would lead to the conclusion that more energy was being absorbed than was actually the case.

4.4.2 Virgin KimWipes®: Normal Incidence

Figure 28 shows the spectral radiative properties for virgin KimWipes® at normal incidence angle. This plot demonstrates the overall spectral nature of the data, which is largely common to all of the sample measurements in this study. In general, the reflectance is seen to play a moderately low role in the radiative behavior of these samples, with peak values between 10%-15% in several spectral areas.

The primary features of this plot involve the transmittance and absorptance. These properties are characterized by widely differing behavior in different spectral regions,

77 corresponding to regions of strong absorption. This behavior is noted in the mid-infrared from 2.8 to 3.1 microns (O-H stretch) and at 3.3 to 3.5 microns (C-H stretch). Another strong, broad absorption band appears between 7 to 9 microns due to C-H in multiple

Radiative Properties of Virgin KimWipes Inside Sphere 100% Normal Incidence Transmittance Reflectance

y Absorptance t r

e 75% p o r P

e 50% v i t a i d

a 25% R

0% 0 5 10 15 20 25 Wavelength (microns)

Figure 28: Normal incidence radiative properties of virgin KimWipes®. modes, O-H in-plane bending, and stretches of both C-O and C-O-C. Another broad, unresolved group of absorption bands occurs from between 12 to 18 microns, primarily

42,43 due to ring modes including C-H, CH2 rocking, and O-H out-of-plane bending .

4.4.3 Virgin KimWipes®: Angular Effects

Figure 29 shows the spectral values of transmittance for virgin KimWipes® at incoming incidence angles from normal incidence (0 degrees) to 60 degree incidence. The data shows that the transmittance is monotonically reduced as the incidence angle is increased, across nearly all of the tested spectral range. These changes are as great as 18% in

78 Transmittance of Virgin KimWipes Inside Sphere 100% 0 degree incidence 15 degree incidence 30 degree incidence e 75%

c 45 degree incidence n

a 60 degree incidence t t i 50% m s n a r

T 25%

0% 0 5 10 15 20 25 Wavelength (microns)

Figure 29: Spectral transmittance of virgin KimWipes® at different incidence angles. regions of moderate to high transmittance and as little as 2% in regions of high absorptance.

The reflectance data, shown in Figure 30, shows increases in limited spectral regions as

Reflectance of Virgin KimWipes Inside Sphere 100% 0 degree incidence 15 degree incidence 75% 30 degree incidence e

c 45 degree incidence

n 60 degree incidence a t

c 50% e l f e R 25%

0% 0 5 10 15 20 25 Wavelength (microns)

Figure 30: Spectral reflectance of virgin KimWipes® at different incidence angles.

79 the incident angle is increased, but the magnitude of the changes, even in those regions, is smaller than that of the transmittance data. Significant angular dependence is only seen from 3.5 to 6.75 microns, where monotonic increases of 7% (from normal incidence to 60 degree incidence) are observed, though very small increases of 3 to 4% are also seen between 11 to 13 microns*.

Absorptance of Virgin KimWipes Inside Sphere 100%

e 75% c n a t p

r 50% 0 degree incidence o

s 15 degree incidence b 30 degree incidence A 25% 45 degree incidence 60 degree incidence 0% 0 5 10 15 20 25 Wavelength (microns)

Figure 31: Spectral absorptance of virgin KimWipes at different incidence angles.

The angular dependence of the spectral absorptance data for the virgin material is seen in

Figure 31. Since this data is determined from the subtraction of the reflectance and transmittance data from unity (conservation of energy), the small increase in reflectance

(as the incident angle increases) tends to slightly offset the decrease in transmittance, with respect to the changes in absorptance. The net effect is that the absorptance doesn’t change (with respect to variation in incident angle) as much as the transmittance does, but

* While the stated experimental uncertainty of +/- 5% would typically preclude confidence in such small changes, the well-behaved, monotonic nature of the data across virtually the entire spectrum suggests that, while the absolute value of the data at any point may only have accuracy to +/-5%, the relative uncertainty between data traces is less. This is discussed in greater detail in the Error Analysis, Appendix V.

80 there are still clear monotonic trends, with as much as 8-12% increases in some spectral regions. The trends are most readily apparent at wavelengths longer than 11 microns, though there are several regions (4 to 6 and 7 to 8 microns) where increases are noticeable. Other regions of typically high absorptance (2.8 to 3.2 and 8.5 to 10 microns) show little angular effect, as these regions absorb most available energy regardless of the incident angle.

4.4.4 Angular Dependency: The Effect of Pathlength on Radiative Properties

Some insight can be gained on the angular dependence by examining how the radiative properties change with incident angle at a specific wavelength. This allows the data to be curve-fit at these specific spectral points, yielding an explicit relationship between incidence angle and the radiative property.

Angular Dependence of Radiative Properties of Virgin KimWipes Properties at 5.10 microns 100% (1959 cm-1)

Data point at 90o shows the y

t theoretical limit, IF the sample

r 75%

e material is homogeneous p o r

P Transmittance 50% e

v Absorptance i t a

i Reflectance d

a 25% R

0% 0 15 30 45 60 75 90 Incident Angle (degrees)

Figure 32: Radiative properties of virgin KimWipes® at 5.10 microns. Red data points (transmittance and absorptance) show the theoretical limits at that angle, if the material was homogeneous.

81 Curve-fitting of the radiative properties with respect to incidence angle for virgin

KimWipes® was carried out at 5.1 microns (chosen for comparison since it is a region of moderate values of both transmittance and absorptance). Figure 32 shows the angular, spectral data, as well as the results of these curve fits. Note that the “red” data points at

90 degree incidence are hypothetical data (rather than measured). A 90 degree incident angle (as defined in this work) means that there is a (nearly) infinite straight-line pathlength through the sample that the incoming energy can take. If the incoming energy passes through an infinite thickness, then the absorptance must be 100%, and therefore transmittance and reflectance must be zero. While this physical description of what happens at severe incidence angles would seem reasonable, it will be examined in more detail shortly.

This plot, as well as the plots of the properties over the tested spectral range (Figures 28,

29 and 30) show that the radiative properties vary monotonically but slowly over the tested angular range of 0 to 60 degree incidence angle. The general range of variation over this 60 degree angular range is from 10% to 20% different from that at zero degree incidence. However, if it is assumed that the absorptance must go to 100% at the theoretical 90 degree incidence, there must be significant changes (in at least some spectral regions) over the remaining 30 degree angular range that could not be tested here. For example, the data at 5.1 microns (Figure 31) shows that at 60 degree incidence, the absorptance is 40%. In this case, the absorptance must increase by 60% over the final angular region of 30 degrees if it were to reach 100%.

82 A reasonable explanation of this can be found by examining how the pathlength (through the sample) varies with incident angle. Examination of the geometry shows that the straight-line pathlength will vary as 1/cos α, where αis the incoming incidence angle, as previously defined. Examination of how the straight-line pathlength varies with angle

(Figure 33) shows that for angles up to 60 degrees (the limit of what could be tested in this work), the variation of this pathlength with incidence angle is relatively small. This slow variation is consistent with the observed slowly varying (with respect to incidence angle) radiative properties. At 60 degrees incidence, the straight-line pathlength is

Pathlength Variation (Straight Line) vs. Incoming Incidence Angle Pathlength varies as 1/cos(a)

10 Pathlength (dimensionless) 8

h

t o g 6 At 60 incoming incidence angle, n

e the pathlength is doubled l h t 4 a P 2

0 0 15 30 45 60 75 90

Incoming Incidence Angle (Degrees)

Figure 33: Variation of straight-line pathlength through a sample as the incidence angle is varied. doubled, whereas at 75 degrees, it would increase by nearly a factor of four. This rapid increase in pathlength for very steep incidence angles would quickly increase the absorptance, and decrease the other properties.

However, the assumption of an undeflected, straight-line path through the sample is not strictly valid. The previously discussed “forward scattering” suggests that, even though

83 the straight-line path through the sample increases dramatically at steep angles, some of the incoming energy would be “forward scattered” out, since the sample is still very thin

(in the normal incidence direction). If the “forward scattering” is assumed to occur on a per unit thickness basis (the original forward scattering measurements were made with normally incident radiation falling on a single thickness of virgin material) and is well characterized, then in principle, a calculation could be made of how much energy would actually “leak though” by means of forward scattering at the theoretical 90 degree incoming incidence angle. However, the low-fidelity of the measurement of the “forward scattering” angular dependence in this study (limited by experimental constraints) means that such an estimate here would be too crude to be useful. Still, the fact that significant energy was noted to be deflected off the straight-line path suggests the interesting and non-intuitive possibility that, for very thin samples such as KimWipes® (which are neither optically thin nor thick in the normal incidence direction), the absorptance may never be 100%, even at very steep incidence angles. However, a material of similar structure but having sufficient dimensional thickness to be considered optically thick would exhibit a different behavior. Such a material would absorb all incoming energy

(except that lost to surface reflections) at all incident angles until the difference between the incident angle and normal would be equal to half of the forward scattering collection angle (as defined in this experiment). At that point, some of the energy that was partially transmitted and then scattered would be deflected away from the sample, and would therefore be unavailable to be absorbed, much like a surface reflection.

84 4.4.5 Heat-Treated KimWipes®: Normal Incidence

The general spectral behavior of the KimWipes® samples with respect to changes in area density is similar for each of the heat treatment temperatures. Accordingly, only one example will be discussed in detail (all spectral data for comparison cases and final data set are available electronically; see Appendix VI for contact information). The example selected was at a heat treatment temperature of 623 K, with treatment times varying from

10 seconds to 90 seconds. The longest treatment time (90 seconds) corresponds to an area density of 0.46 mg/cm2, which represents a 75% mass loss from that of the virgin sample. The degree to which samples could be heat-treated was limited by the fragility of the samples, after being heated to this extent. This temperature was selected as a means to generate samples of the lowest area density possible, as it provided the best temperature for controlling the area density of the samples; lower temperature heating took very long durations to produce low area density samples, while higher temperature heating reduced the area density too quickly to allow control.

Figure 34 is a plot of area density as a function of heat treatment time for this temperature

(all samples from this temperature shown on this plot, including those not used for spectral examination), showing the linear behavior that was observed at each of the tested temperatures. This data suggests that a zeroth-order pyrolysis model is appropriate, and is used in Section 4.6 to determine values for the activation energy and pre-exponential factor for that model.

85 Area Density vs. Heat Treatment Time 623 K350 Oven C (623 Temperature K) 2.00E-032.00 ) 2 m c / 1.50E-031.50 Area Density g m (

y t i 1.00E-031.00 s

n 0 e D

a 5.00E-040.50 e r A 0.00E+000.00 0 30 60 90 120 Heat Treatment Time (sec)

Figure 34: Area density as a function of heat treatment time at 623 K.

Figure 35 shows the spectral variation of normal incidence transmittance for samples with different area densities, produced with heat treatment of 623 K for varying times.

At this temperature, heating times of up to 40 seconds (corresponding to area density changes of up to about 40%) cause nearly imperceptible changes in the spectral data for wavelengths shorter than 7 microns, with the exception of the narrow region at 5.8 microns (this corresponds to the carbonyl band, discussed in Section 4.4.7). The spectral data for wavelengths longer than 7 microns show increase in transmittance that varies from 4% to 12% at 18.5 microns. Given the uncertainty of the spectral data (estimated at

+/- 5.8%, discussed in Appendix IV), differences between these cases could be considered negligible for wavelengths shorter than 12 microns, after which the separation between the virgin data and that treated for 30 seconds is great enough to be distinguished, when considering the uncertainty. Still, the traces fall in the expected order (i.e., the data for the 10 second treatment falls between that of the virgin sample

86 and the 30 second treatment) for the entire spectral range (excepting the previously noted region at 5.8 microns).

Transmittance of Charred KimWipes Inside Sphere 10 sec, 1.60 mg/cm2 Normal Incidence 30 sec, 1.38 mg/cm2 40 sec, 1.13 mg/cm2 100% 2 Samples charred at 623 K 70 sec, 0.80 mg/cm 90 sec, 0.46 mg/cm2 2

Vrgin KimWipes, 1.85 mg/cm

e 75% c n a t t i

m 50% s n a r T 25%

0% 0 5 10 15 20 25 Wavelength (microns)

Figure 35: Normal incidence transmittance of KimWipes, heat-treated at 623 K for varying times.

The spectral data for the two lowest area densities (0.80 and 0.46 mg/cm2, heat treatment times of 70 and 90 seconds, respectively) show markedly different behavior than those with higher area densities. Both of these samples show significantly greater transmittance across the entire (tested) spectral range than higher density samples. These

‘heavily charred’ samples also show less spectral features than the less charred samples, particularly the most extreme case (0.46 mg/cm2).

Figure 36 shows the spectral reflectance data for the samples heat treated at 623 K, plotted on a 100% scale to demonstrate the relative magnitude of the reflectance, which is small compared to the transmittance across the entire spectral domain.The reflectance data shows little difference between samples of different area densities, within the bounds

87 Reflectance of Charred KimWipes Inside Sphere Normal Incidence 100% Samplescharred at 623 K 10 sec, 1.60 mg/cm2 30 sec, 1.38 mg/cm2 2 75% 40 sec, 1.13 mg/cm

e 70 sec, 0.80 mg/cm2 c 2 n 90 sec, 0.46 mg/cm a 2 t Virgin KimWipes, 1.85 mg/cm

c 50% e l f e R 25%

0% 0 5 10 15 20 25 Wavelength (microns)

Figure 36: Normal incidence reflectance of KimWipes, heat-treated at 623 K for varying times. of experimental uncertainty, with some small exceptions. Still, slight trends can be detected in certain areas. Figure 37 shows the same data plotted against a maximum scale of 20%, so that the details can be more easily seen. Though there are no spectral regions (at normal incidence angle) in which the reflectance exceeded 15%, a substantially higher reflectance is noted for wavelengths shorter than 5 microns. The fact that the reflectance is greater at shorter wavelengths is generally consistent with the idea that the material is fairly reflective at very short wavelengths (i.e., visible light), but in the 2 micron span between the end of the visible wavelengths (about 700 nanometers) and the shortest wavelengths tested here (2.75 microns), the behavior is not explicitly known.

Except within the small region centered at 5.8 microns (the carbonyl band, also noted in the transmittance measurements, discussed later), the data for virgin KimWipes® is nearly identical to that of the samples with the four lowest heat treatment times (10, 30,

88 40 and 70 seconds, corresponding to 1.60, 1.38, 1.13 and 0.80 mg/cm2, respectively), with all data at any given wavelength for each of these tests falling within 3% of each other.

Reflectance of Charred KimWipes Inside Sphere Normal Incidence 20% Samples charred at 623 K 10 sec, 1.60 mg/cm2 30 sec, 1.38 mg/cm2 2 15% 40 sec, 1.13 mg/cm

e 70 sec, 0.80 mg/cm2 c 2 n 90 sec, 0.46 mg/cm a t Virgin KimWipes, 1.85 mg/cm2 c 10% e l f e R 5%

0% 0 5 10 15 20 25 Wavelength (microns)

Figure 37: Normal incidence reflectance of KimWipes,heat treated at 623 K for varying times. Note that the reflectance scale is reduced compared to Figure 36 to show detail of data.

A small difference can be seen between those samples and the most charred sample (90 second treatment time, 0.46 mg/cm2), though the difference is barely discernable within the bounds of experimental uncertainty. This extremely charred sample shows an increase in reflectance of about 7% for the narrow region between 2.7 to 3.6 microns, with a slight difference across most of the rest of the spectral domain, compared to the other samples.

The absorptance shows a strong spectral dependence across the entire test domain. In the mid-infrared, however, substantial absorption occurs by the vibrational modes of the

89 cellulose molecule at specific wavelengths. This process governs the spectral behavior of all of the radiative properties7,13,18, though it is the ‘non-absorbed’ light that is actually detected. Since the absorptance data is calculated using conservation of energy, and the measured reflectance and transmittance, it will reflect the information detailed in the other quantities.

Figure 38 shows the normal incidence spectral absorptance data for the test series heat treated at 623 K. The absorptance is observed to decrease monotonically in all spectral regions as the area density decreases, with the exception of the carbonyl band region.

The highly spectral nature of the data is most evident at higher area densities, with many spectral features decreasing at the lower area densities.

Absorptance of Charred KimWipes Inside Sphere 10 sec, 1.60 mg/cm2 Normal Incidence 30 sec, 1.38 mg/cm2 40 sec, 1.13 mg/cm2 2 100% Samplescharred at 623 K 70 sec, 0.80 mg/cm 90sec, 0.46 mg/cm 2 2 Virgin KimWipes, 1.85 mg/cm

e 75% c n a t p

r 50% o s b A 25%

0% 0 5 10 15 20 25 Wavelength (microns)

Figure 38: Normal incidence absorptance of KimWipes, heat-treated at 623 K for varying times.

The majority of data in this study were collected with the sample mounted inside the sphere. This was done to facilitate the measurement of both the ‘temperature’

90 dependence (as determined by examining samples heat treated at different temperatures and times) and the angular dependence (based on the incident beam angle), since the angular measurements could only be conducted inside the sphere.

4.4.6 Heat-Treated Samples: Angular Effects

As in the comparison of similar area density samples from different heat treatment paths, the angular property dependence is qualitatively similar for samples that were heat treated at different temperatures and times. Accordingly, only the samples designated as the representative data set will be discussed here. The discussion here will be in terms of the angular dependency at each of the discrete area densities listed in Table 6.

Qualitatively, the charred samples at different incidence angles behave with the expected combination of characteristics seen in the normal incidence charred samples, and the angular data from the uncharred samples. No particular effects were noted that were specific only to charred samples at different incidence angles.

Data will be presented for spectral transmittance and spectral absorptance for heat treated samples at different incidence angles. The spectral reflectance data is omitted from discussion here, as the behavior of the reflectance was similar from one sample condition to the next, and the relatively low values of reflectance are not particularly informative.

91 Sample 13: Area Density = 1.62 mg/cm2

100 microns

Figure 39: Magnified view of Sample 13, which has an area density of 1.62 mg/cm2. Sample 13 (imaged in Figure 39), with an area density of 1.62 mg/cm2 represents the lightest charred sample in the set. Figure 40 shows the spectral transmittance for this sample, while Figure 41 shows the spectral absorptance. Much like the angular data for uncharred KimWipes®, data at this incidence angle shows only very slight deviation

Transmittance of Charred KimWipes Inside Sphere 0 degree incidence 100% Sample 13 15 degree incidence KimWipes@ 623 K 30 degree incidence 22 0.001621.62 mg/cm g/cm 45 degree incidence

e 75%

c 60 degree incidence n a t t i 50% m s n a r

T 25%

0% 0 5 10 15 20 25 Wavelength (microns)

Figure 40: Spectral transmittance of Sample 13, with area density of 1.62 mg/cm2, at different incidence angles.

92 from the same data at normal incidence. While the effects of heating the sample (and pyrolyzing away much of the mass) are distinct, the angular effect at such a shallow incident angle (compared to normal incidence) is nearly negligible.

Absorptance of Charred KimWipes Inside Sphere 100%

e 75% c n a t p

r 50% 0 degree incidence o

s 15 degree incidence b Sample 13 30 degree incidence A 25% KimWipes @ 623 K 45 degree incidence 0.001621.62 mg/cm g/cm2 2 60 degree incidence 0% 0 5 10 15 20 25 Wavelength (microns)

Figure 41: Spectral absorptance of Sample 13, with area density of 1.62 mg/cm2, at different incidence angles.

93 Sample 72: Area Density = 1.25 mg/cm2

100 μm microns

Figure 42: Magnified view of Sample 72, which has an area density of 1.25 mg/cm2.

Figure 42 shows sample 72, which represents a moderately charred sample, with area density of 1.25 mg/cm2. The spectral transmittance data for this sample is shown in

Figure 43. The angular dependence of the transmittance is evident, with small differences between normal incidence and 15 degree incidence of only 2 percent across

Transmittance of Virgin KimWipes Inside Sphere 100% Sample 72 0 degree incidence KimWipes@ 648 K 15 degree incidence 1.250.00125 mg/cm g/cm2 2 30 degree incidence e 75% c 45 degree incidence n a

t 60 degree incidence t i 50% m s n a r

T 25%

0% 0 5 10 15 20 25 Wavelength (microns)

Figure 43: Spectral transmittance of Sample 72, with area density of 1.25 mg/cm2, at different incidence angles.

94 most of the spectral domain, which is within experimental uncertainty. This difference increases to 5% to 6% for larger incidence angles, particularly at wavelengths longer than

10 microns. While these differences between the curves are fairly small in light of the estimated experimental uncertainty, some credence is given to these differences since the data falls within monotonic trends across virtually the entire spectrum. This attribute is common to nearly all of the data traces for different incidence angles for the same sample.

Figure 44 displays the spectral absorptance for this sample. Again, the angular trends are similar to those previously seen, except that the absorptance takes on slightly lower values, compared to the Sample 13.

Absorptance of Virgin KimWipes Inside Sphere 0 degree incidence 15 degree incidence 100% 30 degree incidence 45 degree incidence 60 degree incidence

e 75% c n a t p

r 50% o s

b Sample 72

A 25% KimWipes @ 648 K 0.001251.25mg/cm g/cm2 2 0% 0 5 10 15 20 25 Wavelength (microns)

Figure 44: Spectral absorptance of Sample 72, with area density of 1.25 mg/cm2, at different incidence angles.

95 Sample 82: Area Density = 0.77 mg/cm2

100 microns

Figure 45: Magnified view of Sample 82, which has an area density of 0.77 mg/cm2. This sample represents a heavily charred condition having an area density of

0.77 mg/cm2, with an image of this sample in Figure 45. Samples that had area densities below 1.00 g/cm2 tended to be more difficult to work with, due to their fragile structure, and also showed less consistency in their spectral results than the lesser charred samples.

This is evident in Figure 46, which shows the spectral transmittance for this sample.

Transmittance of Charred KimWipes

Inside Sphere 0 degree incidence KimWipes @ 673 K 15 degree incidence 100% 2 2 0.000770.77 mg/cm g/cm 30 degree incidence Sample 82 45 degree incidence

e 75% 60 degree incidence c n a t t i 50% m s n a r

T 25%

0% 0 5 10 15 20 25 Wavelength (microns)

Figure 46: Spectral transmittance of Sample 82, with area density of 0.77 mg/cm2, at different incidence angles.

96 This plot shows similar trends as those seen previously for all incidence angles except 60 degrees incidence. That angle shows a 10% to 20% reduction from the 45 degree incidence test (with the greater difference evident at longer wavelengths), whereas previous tests had shown the differences between 45 degrees and 60 degrees (incidence) to be 5% to 12%.

As previously mentioned, the 60 degree incidence tests were carried out with a different sample than the one used for each of the angles between normal incidence and 45 degrees incidence. This was due to the fact that the sample was gradually damaged as it was mounted and removed for each of the lower incidence angles, typically leaving the remnant to be too small for mounting on the 60 degree sample holder (which had the largest area to be covered). This problem was noted early on during testing, so extra samples were made under the same conditions, to produce an area density as close as possible to that of the sample used for incidence angles from normal to 45 degrees. The samples used for the 60 degree incidence testing were chosen to be within 5% of the target value.

The previously discussed spectral transmittance data from samples 13 and 72 (Figure 40 and Figure 43, respectively) does not show the disparity between 45 degrees and 60 degrees incidence that was demonstrated in Figure 46 for sample 82. This suggests that for Samples 13 and 72, the substitution of a similar sample in the 60 degree incidence test provided reasonable and expected results. However, the comparatively large gap

97 between 45 degree incidence (sample 82) and 60 degree incidence (sample 86, which had a similar area density to sample 82, used for the 60 degree test) suggests a discrepancy.

The area density measurements of 0.77 mg/cm2 and 0.81 mg/cm2 (respectively) are within 5% of each other; previous results suggest that area densities within this range show negligible spectral differences. No explanation for this discrepancy is given, except to suggest that the spectral property measurements may become more sensitive to small changes in area density as the area density decreases below 1.00 g/cm2.

Absorptance of Charred KimWipes

Inside Sphere 0 degree incidence 100% 15 degree incidence 30 degree incidence 45 degree incidence 60 degree incidence

e 75% c n a t p

r 50% o s b

A 25% KimWipes@ 673 K 2 0.000770.77 mg/cm g/cm2 Sample 82 0% 0 5 10 15 20 25 Wavelength (microns)

Figure 47: Spectral absorptance of Sample 82, with area density of 0.77 mg/cm2, at different incidence angles.

Figure 47 shows the results of the spectral absorptance at different incident angles for

Sample 82. Since the absorptance data is calculated (rather than directly measured) and is based on both the transmittance and reflectance data, the substantial difference in absorptance between 45 degree and 60 degree incidence is not surprising, in light of the previous discussion.

98 Sample 29: Area Density = 0.40 mg/cm2

100 microns

Figure 48: Magnified view of Sample 29, which has an area density of 0.40 mg/cm2. Sample 29 is the last element in the final dataset, imaged in Figure 48. This sample represents the highest degree of charring of all samples in the dataset, with spectral data indicative of such a great degree of pyrolysis. The image of the sample demonstrates that much of the sample has been pyrolyzed away, with dramatic void areas between the

Transmittance of Virgin KimWipes Inside Sphere Sample 29 100% KimWipes@ 623 K 0.000400.40 mg/cm g/cm2 2

e 75% c n a t t i 50% m 0 degree incidence s

n 15 degree incidence a

r 30 degree incidence

T 25% 45 degree incidence 60 degree incidence 0% 0 5 10 15 20 25 Wavelength (microns)

Figure 49: Spectral transmittance of Sample 29, with area density of 0.40 mg/cm2, at different incidence angles. This sample represents the most severely charred sample in the dataset.

99 remaining charred fibers. The effect this has on the spectral property values is shown in

Figure 49 which represents the spectral transmittance for this sample at different incidence angles.

This data shows a general trend similar to that from Figure 46, which showed the spectral transmittance for Sample 82 (0.77 mg/cm2). The sample experiences a loss in spectral features at longer wavelengths as the degree of pyrolysis increases, as well as a general decrease in transmittance across the spectral domain.

Further, the large difference between the 45 degree incidence data and the 60 degree incidence data is seen in this sample, as it was in sample 82, with a difference of 15% seen between those incidence angles for wavelengths greater than 5 microns.

As previously discussed, the sample used to acquire the 60 degree incidence curve was different than the one used to acquire all the other incidence angle data. In this case, a difference in area density of 4.1% existed between sample 82 (0.40 mg/cm2), used for incidence angles from normal through 45 degrees, and sample 31 (0.41 mg/cm2), used for the 60 degree incidence case. While differences of 4% in area density seemed to have a lesser effect on light to moderately charred sample 13 (1.62 mg/cm2) and sample 72

(1.25 g/cm2), the more severely charred samples appear to be more sensitive to this.

Still, experimental circumstances forced the use of a separate (but similar) sample for the

60 degree incidence data, and the data must simply be evaluated with this in mind.

100 Absorptance of Virgin KimWipes

Inside Sphere 0 degree incidence Sample 29 15 degree incidence 100% KimWipes @ 623 K 30 degree incidence 2 2 0.000400.40 mg/cm g/cm 45 degree incidence 60 degree incidence

e 75% c n a t p

r 50% o s b

A 25%

0% 0 5 10 15 20 25 Wavelength (microns)

Figure 50: Spectral absorptance of Sample 29, with area density of 0.40 mg/cm2 at different incidence angles.

Figure 50 shows the spectral absorptance for sample 29. Similar to sample 82, only small changes are seen between incidence angles up to 45 degrees, but the large change in the transmittance data manifests itself in the calculated spectral absorptance data. The overall magnitude of the absorptance is seen to be the lowest of all the samples, which is consistent with this sample having the lowest area density. Very few spectral features are present except between 3 to 9 microns, which shows several sharp peaks but little else.

4.4.7 Spectral Changes in the Carbonyl Band

While changes have been seen in many spectral regions (as samples of different area density are compared to each other), many of these spectral features are broad in their scope, and cannot easily be classified as relating only to one functional group of the

101 cellulose. Further, these broad spectral changes tend to be proportional to changes in the area density, independent of the thermal history of the sample.

Absorptance of Charred KimWipes at Normal Incidence Angle 100% Carbonyl Band

e 75% c n a t p

r 50% o 2 s 1.85 mg/cm b Carbonyl Band 1.62 mg/cm2 A 25% 1.25 mg/cm2 0.77 mg/cm2 0.40 mg/cm2 0% 5.0 5.5 6.0 6.5 7.0 Wavelength (microns)

Figure 51: Absorptance in the carbonyl band (centered at 5.8 microns) for KimWipes® at different area densities (normal incidence). Absorptance in this band increases as the area density decreases, until the area density reaches 0.001 g/cm2, then decreases slightly.

However, one spectral region indicates something different. The narrow spectral region from 5.5 to 6.7 microns shows a dramatic trend reversal in all of the radiative properties, compared to the general trends seen in other spectral regions (i.e., absorptance typically decreases as the area density decreases). Figure 51 shows a plot of the normal incidence spectral absorptance for the region from 5 to 7 microns. The region of the greatest difference is centered at 5.8 microns, corresponding to absorption by a carbonyl group.

Here, the absorptance is seen to increase rapidly between the virgin sample and the mildly pyrolyzed samples, and then change more slowly as the samples’ area density continues to decrease to 1.25 mg/cm2. This is because the absorptance in this region increases to an approximate equilibrium value between the formation of carbonyl groups

102 and their ultimate decomposition into carbon dioxide. A slight decrease in the absorptance is then seen as the area density continues to decrease below 1.00 mg/cm2.

This is consistent with the interpretation that as the rate of carbonyl production (which caused the increase in absorptance) from uncharred material is now less than the decrease in absorptance due simply to mass loss. The extent of the change in absorptance reaches a peak value of about 30% absolute difference between the virgin material and that of the sample with area density of 1.25 mg/cm2 at 5.8 microns.

4.4.8 Void Spaces between Fibers and their Effect on the Radiative Property Values

As previously discussed, KimWipes® are composed of a mat of loosely woven fibers, causing void spaces between fibers. Some of these voids are large enough to see with the naked eye, and can easily be distinguished with a microscope. While this work treats

KimWipes® from a ‘macroscopic’ viewpoint (i.e., the material is treated as though it is homogenous), the non-homogeneous nature of the material plays a considerable role in shaping the macroscopic behavior.

The extent of voids in the sample was quantified by digitizing, then thresholding the magnified images of the samples. For this purpose, all samples were imaged at the same magnification on a gold microscope slide, with the same illumination. The color images were then converted to grayscale, and a constant threshold value was applied to all images. Using this technique, all pixels corresponding to voids in the sample were converted to an 8-bit value of 255, while all remaining pixels (corresponding to fibers)

103 were converted to a zero value. Pixels were counted, and the ratio of high value pixels to the total number of pixels in the image then represents a void fraction.

The spatial extent of a pixel was determined by imaging an object of a known distance with the same imaging configuration, then counting the number of pixels corresponding to a known spatial distance in that image. This was carried out and a scale factor of 0.94 microns/pixel was determined. This means that even a single pixel that is thresholded to a ‘high’ value would be deemed to correspond to a void of at least 0.94 microns. Spaces that are smaller than this minimum size could not be thresholded. Given that the thresholded areas correspond to voids of at least a single pixel size (generally more than a single pixel), wavelengths that are smaller than this size will pass directly through these areas represented by the thresholded values without interacting with the material. Since voids of sizes smaller than the pixel resolution of the image cannot be imaged, these small voids can exist without being measured. However, since the size of an undetectable void is smaller than the shortest wavelengths measured for this experiment, the assumption is made that voids smaller than this resolution would have no effect on the radiative property measurements that were carried out for this study.

Figure 52 shows a plot of void fraction as a function of area density, with Figure 53 showing the thresholded images of the final dataset. Evidence of holes can be seen in all of the samples, but are especially prevalent as the area density decreases. The data shows that the fraction of voids actually decreases slightly (from 10.2% to 7.5%), as the sample undergoes the first stages of mass loss. From a physical standpoint, KimWipes® have

104 long been observed to shrink as they are initially heated, causing problems in combustion tests in which tightly mounted samples (for example, samples that are stretched taut then taped into place on a sample holder) tend to shrink to the point that the samples can tear.

This contraction is demonstrated in the behavior of lightly charred samples, in which the void fraction initially decreases despite losing mass.

After this initial contraction, the void fraction then continues to increase throughout the remaining char history. The most charred sample had a void fraction of 30%, showing that 3 times as much light would pass directly through this sample (compared to the virgin sample), without interaction with the material.

Area Percentage of Voids Between Fibers Charred KimWipes

Data acquired by thresholding 30%

dgital images, then integrating e

and ratioing the areas g a t

corresponding to fibers and 20% n

voids e c r e P

10% d i o V 0% 0.0020 0.0015 0.0010 0.0005 0.0000

Area Density (g/cm2)

Figure 52: Void fraction as a function of area density for charred KimWipes.

This behavior means that there are two mechanisms by which the transmittance increases with decreasing area density. As the material chars, the individual fibers lose mass, and become dimensionally thinner, allowing more of the light that strikes the fiber to pass

105 Virgin KimWipes (KW) Sample 0 1.85 mg/cm2 Void Fraction: 10.2%

Lightly Charred KW Sample 13 1.62 mg/cm2 Void Fraction: 7.5%

Moderately Charred KW Sample 72 1.25 mg/cm2 Void Fraction: 11.5%

Heavily Charred KW Sample 82 0.77 mg/cm2 Void Fraction: 17.5%

Severely Charred KW Sample 29 0.40 mg/cm2 Void Fraction: 29.5%

Original Images Thresholded Images Figure 53: Grayscale visual images and thresholded analysis images of samples in final data sample set. The thresholded images faithfully reproduced the areas of voids, and allowed calculation of the total void fraction for each image. through. Also, though the fibers initially contract and become closer to each other, they reach a point where they have contracted the maximum amount possible. As they continue to pyrolyze, the fibers continue to shrink in size without further contraction, causing significant increases in void spaces. This combination of factors contributes strongly to the increase in transmittance, and accounts for the largest part of the decrease in absorptance.

106 4.4.9 Comparison of Heat-Treated Samples with Burned Sample

Comparison was made between the samples that were produced by heat-treating in the oven to a sample created by a near-limit, upward spreading (concurrent flow) flame that self-quenched. Due to the difficulty of producing a sample of sufficient size and uniformity for FTIR testing through near-limit quenching, only one case could be examined. Still, this case provides an interesting comparison between the results obtained using the prepared samples from this study and those obtained using a burned sample.

The burned sample was created by burning a single sheet of KimWipes® in a normal gravity, upward burning configuration at 21% O2, at a pressure of 4.0 psia, using a hot- wire ignition system. Once the sample was ignited, the pressure was reduced (as rapidly as the attached vacuum pump could provide) so that the pressure extinction limit would be reached. This condition provided a self quenching flame that propagated about 8 cm past the igniter, and left a pyrolysis region that was approximately 3 cm long, though this remaining char was cracked near the burnout front, and was not uniform in appearance in the downstream direction (as is typical).

Due to the nature of the FTIR instrument and the width of the beam at the sample plane

(described in Section 3.2.4), a uniform sample (with respect to the degree of pyrolysis) of about 1 cm in diameter was required. While a uniformly charred sample of that diameter was not available from the burned sample, the most uniform, a 1 cm diameter region that

107 was determined by visual inspection to be the most appropriate was cut from the sample

(Figure 54). While this section was the best available, a visual gradient in the color of the sample was detected, indicating that the region was not completely uniform. Since a gradient existed within the region covered by the light beam of the FTIR, the results represent a spatially averaged value over the range of pyrolysis conditions in that region.

Figure 54: Image of burned and quenched sample used for comparison with heat treated samples.

The area density for the selected region of the burned sample was determined using the methods described in Section 3.1.2, and was found to be 1.42 mg/cm2. Spectral data for this sample was acquired using the inside the sphere, normal incidence method, described in Section 3.2.4. That data is presented in Figure 55, which also shows the normal incidence data for samples numbered 13 and 72 (area densities of 1.62 and

1.25 mg/cm2, respectively).

108 Absorptance of Charred KimWipes 100% at Normal Incidence Angle

75% e c n a t p

r 50% o s b A 25% 1.62 mg/cm2 (oven) 1.25 g/cm2 (oven) 2 1.42 mg/cm (burned) 0% 0 5 10 15 20 25 Wavelength (microns)

Figure 55: Comparison of normal incidence spectral absorptance between burned and heat-treated KimWipes®.

Examination of this plot shows that the data from the burned sample closely that from sample 13, which had an area density of 1.62 mg/cm2 (about 11% difference). All three data sets are within 4% of each other for wavelengths shorter than 13 microns, after which the data from the burned sample most closely resembles that from sample 13. All important spectral features are present in both the burned and heat-treated samples, and the agreement with sample 13 is within experimental uncertainty.

Ideally, the spectral data at long wavelengths for the burned sample would be expected to fall between the data for samples 13 and 72, since its area density is between them.

However, the uncertainty associated with each of the data traces makes fine determinations difficult. Further, the non-uniformity of the burned sample complicates the interpretation of the data, as the data from that sample represents a spatial average of a non-uniform material. Still, when considering the differences in thermal history that the burned sample had versus that of the oven-treated samples, this data supports the

109 conclusion (reached in Sections 4.2 and 4.3) that the general spectral behavior of the samples is a function of their area density, rather than their thermal history.

4.5 Band Integrated Data Results

4.5.1 Integration of Representative Data Set

Current generation numerical combustion models of multi-dimensional flame spread are unable to make use of spectrally resolved surface radiative properties. Therefore, the spectral data from the representative data set from this study were integrated over a broad spectral band at a variety of temperatures, to give appropriate data for overall heat transfer calculations (Appendix V). As an example of these results, Section 4.5.2 presents data that is integrated over the area density and temperature conditions predicted by the model23 seen in Figure 15. Note, however, that the numerical combustion model used in that correlation did not employ either the radiative properties developed here, or the new values of pre-exponential factor and activation energy that were developed in this study. This means that the surface temperatures which were chosen to use for the spectral integrations of each sample may not be correct. To properly account for these factors, the spectral data (at each angle) must be integrated at all potential temperatures, creating a ‘look-up’ table that the combustion model (employing the values of activation energy and pre-exponential factor) can then employ. This table (found in Appendix V) provides band integrated data from each pyrolysis level at a variety of possible Planck function temperatures. Since the choice of which temperature to choose for the integrations may be affected by the application of the data, an iterative process may need

110 to be performed by the model in which an initial ‘guess’ is made as to which combination of area density and Planck function temperature is appropriate. The integrated value from that combination would be used, and then the temperature and area density at that spatial point could be re-evaluated, to see if a different radiative value would be required.

This process would continue until a converged value is reached (i.e., a calculated surface temperature and area density that is comparable with the conditions used in the band integration).

4.5.2 Example of Band-Integrated Data

As an illustration of how this data could be applied, the integrated data is presented for an example case. The spectral data set chosen for each of the integrations was selected by matching (as closely as possible) the combination of samples of different area densities with Planck temperatures that the previously mentioned numerical model predicts will yield such an area density (Figure 15). This process was then repeated for each of the angular data sets, yielding a table of data at different temperatures and angles. This representation of angular dependent emittance data is shown in Table 8, along with the fraction of energy that the spectrally integrated band represents of the total energy at the given temperature*.

* Note that Table 8 was developed using a numerical model which did not employ the new values of pre- exponential factor or activation energy. The data in Appendix V is recommended for use in real applications, as described in Section 4.5.1.

111 The band integrated values were determined by integrating the spectral data from 2.50

μm to 24.93μm using the representative data at a series of different temperatures ranging

(in 25 K increments) from 300 K to 750 K. Calculations show that this spectral range accounts for 78% to 93% of the total energy that can be emitted, depending on the temperature.

Temp (K) Sample Area ε@ 0 ε@ 15 ε@ 30 ε@ 45 ε@ 60 Fraction of # Density degree degree degree degree degree energy in (mg/cm2) incidence incidence incidence incidence incidence spectral band 300 0 1.85 0.699 0.709 0.725 0.744 0.788 78.2% 325 0 1.85 0.692 0.702 0.717 0.736 0.780 81.6% 350 0 1.85 0.683 0.694 0.708 0.727 0.770 84.4% 375 0 1.85 0.674 0.685 0.699 0.717 0.760 86.4% 400 0 1.85 0.664 0.675 0.689 0.707 0.750 88.3% 425 0 1.85 0.655 0.666 0.679 0.697 0.739 89.7% 450 0 1.85 0.645 0.656 0.669 0.687 0.729 90.9% 475 0 1.85 0.636 0.647 0.660 0.677 0.720 91.8% 500 0 1.85 0.627 0.639 0.651 0.668 0.711 92.5% 525 0 1.85 0.619 0.631 0.643 0.660 0.703 92.9% 550 0 1.85 0.612 0.624 0.636 0.653 0.695 93.2% 575 0 1.85 0.606 0.618 0.630 0.646 0.688 93.3% 600 13 1.62 0.571 0.595 0.632 0.645 0.710 93.2% 625 72 1.25 0.549 0.569 0.594 0.610 0.649 93.0% 650 82 0.77 0.446 0.462 0.488 0.511 0.617 92.6% 675 29 0.40 0.379 0.359 0.399 0.441 0.520 92.1% 700 29 0.40 0.376 0.356 0.397 0.438 0.516 91.4% 725 29 0.40 0.374 0.354 0.395 0.435 0.512 90.7% 750 29 0.40 0.372 0.352 0.393 0.432 0.509 89.8% Table 8: Band integrated emittance values of charred KimWipes at different incidence angles. The spectral data used for these integrated results was selected from the final data set to the area density/temperature relationship that a numerical combustion model predicted.

Figure 56 is a plot of the emittance values shown in Table 8. The family of curves show the band integrated emittance as a function of temperature at each of the tested angles.

This plot shows the overall behavior of the emittance to be decreasing with temperature at each angle, with a sharp decrease taking place from 600 K to 675 K. Generally, the emittance is seen to increase as the viewing angle increases.The 0 degree incidence and

15 degree incidence data traces converge and then cross at about 675 K, but the

112 Band Integrated Emittance Different Incidence Angles

0 degree incidence 80% 15 degree incidence 30 degree incidence

d 70% 45 degree incidence e t

e 60 degree incidence a r c

g 60% n e a t t t n i

I Spectral data used in these 50% m d band integrated values E n a 40% acquired from KimWipes at B different levels of pyrolysis 30% 300 400 500 600 700

Temperature (K) Figure 56: Example of broadband integrated emittance vs. temperature for different incidence angles. difference between the traces never exceeds about 2%, which is within the expected experimental uncertainty of +/- 3.2% (discussed in Appendix IV).

A significant feature of the broadband integrated data is seen in the vicinity of 575 K –

600 K. This is the only region where the data varies non-monotonically, with the absorptance (which generally decreases as temperature increases) experiencing a slight increase with temperature until about 600 K, at which point it resumes its decline. This effect is more pronounced as the incidence angle is increased, with a smooth trend across the different angles. The increase is a maximum of about 7% above what the expected trend line would indicate, for the 60 degree incidence case. This effect is explained by the combination of the shift of the peak in the Plank curve towards shorter wavelengths at higher temperatures, and the choice of which data set to use at each temperature. As previously discussed, the choice of which sample’s spectral data to use for the band integrated value (for this example) was determined by examining the numerical models’

113 prediction of area density as a function of temperature (Figure 15), and choosing a sample with an area density closest to that which the model predicts would exist at the temperature to be integrated. Examination of Figure 15 shows that the temperature range from 575 K to 675 K is a region in which the area density drops sharply. This means that spectral data from different samples was used between the integrations at 575 K and 600

K. According to the numerical results, the virgin KimWipes® data (area density

1.85 mg/cm2) is still appropriate for the 575 K case, since very little mass loss has taken place up to that temperature. By the time the material reaches 600 K, the sample with area density of 1.62 mg/cm2 (sample 13) best matches the predicted area density. This aspect, when combined with both the change in incidence angle and the change in the shape of the Planck curve, results in the unexpected behavior seen in Figure 56.

To understand this, consider that at 575 K, the peak of the Planck curve occurs at

λpeak=5.04 microns. At this wavelength, the spectral absorptance (from the virgin

KimWipes®, with an area density of 1.85 mg/cm2, which most closely matches what the model predicts at that temperature) at normal incidence is 0.33, while at 60 degree incidence it is 0.37. However, the peak of the Planck curve shifts to at λpeak=4.84 microns, while the spectral data is now taken from sample 13, with an area density of

1.62 mg/cm2. Using that sample, the normal incidence absorptance is equal to 0.33 (the same value at normal incidence for the virgin material), while the 60 degree incidence absorptance for this sample has climbed to 0.47 (from 0.37 for the virgin sample). Since the spectral values that fall under the peak of the Planck curve are weighted that greatest in the broad-band integration, the integrated value of absorptance can change from one

114 incidence angle to another as the temperature changes. Further discussion on how increasing temperature affects the band integrated values can be found in Appendix III.

4.5.3 Application of Kirchoff’s Law to Band-Integrated Properties

The application of band-integrated radiative property values to heat transfer calculations often involves the use of Kirchoff’s Law, since it is generally the absorptance that is measured, but the emittance that is needed (often, in addition to the absorptance).

A common misconception (and misuse) of Kirchoff’s Law is the simple statement that

“emittance is equal to absorptance”. While this is true under some circumstances, this rule actually states that at similar wavelengths, temperatures, and viewing angles, the absorptance is equal to the emittance. However, real configurations rarely provide the needed equalities to validate the use of Kirchoff’s Law with band integrated properties.

The total (band-integrated) emittance of a material is related only to its material composition, its surface finish, its optical pathlength (or “thickness”), viewing angle, and its temperature. The total absorptance, however, is not explicitly dependent on the material’s temperature, but rather on the incoming radiative flux*.

If the materials that are exchanging radiation have different spectral properties, it is easy to understand that spectral regions of high emission from one material could correspond

* There is, of course, an indirect dependence on the material’s temperature, insofar as its temperature can affect its composition, surface finish, and potentially its thickness, through pyrolysis.

115 to a region of low absorptance in the other. However, this can happen even between identical materials if the materials are at different temperatures. In that case, all of the radiative flux leaving from one may not be absorbed by the other (even if they have the same spectral property values). This is due to the previously discussed shift of the peak of the blackbody curve with temperature; if the two materials are at different temperatures, the differing shapes of the two respective Plank curves will weight the spectral contributions of absorptance and emittance differently. Clearly, this effect will increase as the temperature difference between the materials increases.

In a slightly different example, a difference between the broad band emittance and absorptance can occur if one of the radiating entities (in the solid fuel combustion problem, either the surface or the gas) is spectrally uniform. This situation can be encountered in combustion problems when soot is present (entrained in the gas phase), which behaves as an approximately spectrally uniform emitter at a temperature much greater than that of the surface.

Further, two materials that have similar total emittance (at a given temperature) may absorb radiation from a spectral source differently, as the spectral distribution of the emittance values may be different, even though at the given temperature, they integrate to the same value. This can be encountered when using published values of band integrated properties, as they are generally calculated (unless otherwise noted) at the same temperature. For all of these reasons, the use of Kirchoff’s Law with band integrated values is generally not valid, as the spectral distribution and temperature of both bodies

116 that are radiatively interacting must be accounted for. The subsequent section describes a theoretical configuration in which the band integrated absorptance is different than the band integrated emittance for a given material.

4.5.4 Example Use of Band Integrated Data: Radiative Coupling

One example of a case in which the integrated absorptance is not equal to the integrated emittance occurs in concurrent flow flame spread over a thin solid fuel. The fuel surface temperature cannot exceed the temperature at which the material is vaporized, which is likely to be much less than temperatures in the gas phase. Additionally, the spectral properties of the surface are likely to be very different from those of the gas phase species, which generally have sharp distinctions between spectral regions of high and low emittance.

The coupling between the gas and the surface is demonstrated by modeling the gas phase as a uniform layer (1 cm thick) of a homogeneous mixture of 8% mol fraction (each) of

* CO2 and H2O and 1% mol fraction of C2H6 (balance N2) with a temperature of 1200 K at

1 atm pressure. These conditions are used as representative of average conditions seen in a concurrent flow, low-speed flame, with data taken from the model of Jiang5. While it is recognized that the concentrations and temperatures of gasses in a combustion configuration are spatially dependent, these simplification were needed to allow calculation of the spectral properties of the gas mixture. The gas-phase spectral data for

* C2H6 was used to model the hydrocarbon gasses that are ejected from the fuel surface, as this is the largest hydrocarbon molecule listed in the HITRAN/HITEMP databases.

117 these conditions was generated using the HITEMP database for both CO2 and H2O, and the HITRAN data for C2H6. This data allowed a heat flux to be calculated by applying that data to a blackbody curve for the desired temperature.

Figure 57 is a plot of the spectrally resolved emittance from this gas model (shown in red), as well as the spectral absorptance from virgin KimWipes® (sample 0, 1.85 mg/cm2, area density, shown in blue) and severely pyrolyzed KimWipes® (sample 29,

0.40 mg/cm2 area density, shown in black). Examination of this plot shows that the spectral regions of strong absorptance for the surface do not correspond to regions of strong spectral emittance from the gas. An example of this is the region from 8 to 12 m, where the surface is a fairly strong, broad-band absorber, but the gas emits very little.

Spectral Emissive Power for KimWipes Spectral Data for Virgin & Charred KimWipes

6000 100%

e 5000 v i ) e s 75% c m s i n m

4000 a * m t 2 t i E m l / m a

r 3000 50% E W t ( c e r l e e p p

w 2000 m S o 25% a s P S a 1000 G

0 0% 0 5 10 15 20 25 Wavelength (microns)

CO2, H2OCO2, and H2O C2H6 and mix C2H6 at 1200 mix atK 1200 K Virgin KimWipes:Virgin KimWipes: 0.001847 g/cm2 1.85 mg/cm2 SeverelySeverely Charred Charred KW: KW:0.000395 0.40 g/cm2mg/cm2 Figure 57: Spectral emittance of virgin and severely charred KimWipes®, as well as the spectral emissive power of a gas mixture of 8% H 2O, 8% CO2, and 1% C2H6 at 1200 K, with a 1 cm pathlength. The spectral region of highest incoming radiative flux occurs in a spectral region in which the surface absorbs relatively little, compared to its overall emittance.

118 Also, changes in the spectral absorptance of the solid caused by differences in the degree of pyrolysis are shown in a narrow region around 4.3 m, and in the broad region from

13m to 17 m. The 4.3 m band is a narrow but very strong CO2 emission band in which both the unpyrolyzed and the severely pyrolyzed samples can only absorb about

20%-35% of the emitted radiation from the gas. However, in the broad region from

13m to 17 m (which in the gas model is a band made up of a combination of CO2,

H2O, and C2H6), the unpyrolyzed sample absorbs between 65% of the limited incoming energy, while the severely pyrolyzed sample only absorbs about 30%.

Overall results are shown in Table 9, along with results of a sensitivity study in which a limited parametric examination was made of the effect of changing the pathlength, temperature, and concentration of the gas constituents. The effect of gas pathlength was studied by calculating the flux with path lengths of 1 cm, 5 cm, and 10 cm, while holding the other variables constant. Likewise, the concentration was discretely varied at three concentration levels with constant pathlength and temperature, and two temperatures were studied with constant concentrations and path lengths.

Comparison of the broadband integrated emittance with the integrated absorptance occurring as a result of different gas mixtures shows that in none of the calculated cases does the band integrated emittance equal the band integrated absorptance. Further, these results demonstrate that since the spectral flux from the gas is a strong function of the optical pathlength through the gas (with much smaller effects due to changes in concentration and temperature, within the range that these variables were perturbed), the

119 band integrated absorptance is also a function of these variables. These calculations show that in certain practical conditions such as a flame spread configuration, the band- integrated emittance and absorptance for a given material may not be equal, without violating Kirchoff’s Law.

Temp Sample # Area Integrated Integrated Integrated Integrated Integrated Integrated Integrated (K) Density Emittance Absorptance Absorptance Absorptance Absorptance Absorptance Absorptance (mg/cm2) vs Gas Mix 1 vs Gas Mix 2 vs Gas Mix 3 vs Gas Mix 4 vs Gas Mix 5 vs Gas Mix 6

300 0 1.85 0.699 0.429 0.451 0.470 0.418 0.441 0.450 325 0 1.85 0.692 0.429 0.451 0.470 0.418 0.441 0.450 350 0 1.85 0.683 0.429 0.451 0.470 0.418 0.441 0.450 375 0 1.85 0.674 0.429 0.451 0.470 0.418 0.441 0.450 400 0 1.85 0.664 0.429 0.451 0.470 0.418 0.441 0.450 425 0 1.85 0.655 0.429 0.451 0.470 0.418 0.441 0.450 450 0 1.85 0.645 0.429 0.451 0.470 0.418 0.441 0.450 475 0 1.85 0.636 0.429 0.451 0.470 0.418 0.441 0.450 500 0 1.85 0.627 0.429 0.451 0.470 0.418 0.441 0.450 525 0 1.85 0.619 0.429 0.451 0.470 0.418 0.441 0.450 550 0 1.85 0.612 0.429 0.451 0.470 0.418 0.441 0.450 575 0 1.85 0.606 0.429 0.451 0.470 0.418 0.441 0.450 600 13 1.62 0.571 0.387 0.410 0.429 0.377 0.398 0.409 625 72 1.25 0.549 0.380 0.402 0.421 0.370 0.391 0.402 650 82 0.77 0.446 0.297 0.316 0.333 0.289 0.306 0.315 675 29 0.40 0.379 0.278 0.294 0.307 0.271 0.285 0.293 700 29 0.40 0.376 0.278 0.294 0.307 0.271 0.285 0.293 725 29 0.40 0.374 0.278 0.294 0.307 0.271 0.285 0.293 750 29 0.40 0.372 0.278 0.294 0.307 0.271 0.285 0.293 Gas Mixture Conditions Mix 1: 8% CO2 8% H2O 1% C2H6 1 cm pathlength 1200 K 1 atm Mix 2: 8% CO2 8% H2O 1% C2H6 5 cm pathlength 1200 K 1 atm Mix 3: 8% CO2 8% H2O 1% C2H6 10 cm pathlength 1200 K 1 atm Mix 4: 6% CO2 6% H2O 0.5% C2H6 1 cm pathlength 1200 K 1 atm Mix 5: 12% CO2 12% H2O 2% C2H6 1 cm pathlength 1200 K 1 atm Mix 6: 8% CO2 8% H2O 1% C2H6 1 cm pathlength 1000 K 1 atm

Table 9: Band-integrated emittance and absorptance for KimWipes® with a variety of calculated incoming spectral flux conditions. Integrated emittance values were developed using area density & temperature data from the numerical model discussed in Section 4.5.1.

120 4.5.5 Narrow Band (Imaging Space) Integrated Values

Another application of band-integrated data lies in thermal imaging. Just as in numerical calculations, accuracy in radiometric thermal imaging is dependent on accurate knowledge of the targets’ radiative properties (in this case, emittance).

In concurrent flame spread experiments, the fuel surface must be imaged through the gas phase flame. This requires spectral filtering to remove the effects of spectral emitters

Spectral Transmittance of Approximate Combustion Gas Mixture 100%

90%

e Transmittance of gas c

n mixture

a 80% t t i

m 7-14μm 3-5μm 8%mol fraction CO s 70% band 2 n band 8%mol fraction H 0

a 2 r

T 1%mol fraction C H 60% 2 6 1200 K, 1 atm 1 cm pathlength 50% 0 5 10 15 20

Wavelength (microns)

Figure 58: Calculated spectral transmittance of gas mixture used to model combustion gasses, showing MWIR and LWIR bands that are used for thermal imaging. such as CO2 or H2O. Broad-band emitters (such as soot) present more difficulty, in that the radiation from such a source cannot be removed by spectral filtering. Some efforts have been made to account for radiation from soot for some cases31, but the underlying problem of accounting for the surface’s radiative characteristics remains. The present application of the spectral data for the fuel surface assumes that the spectral filtering has removed all gas phase radiation.

121 Figure 58 is a plot of the spectral transmittance from the mixture of CO2, H2O and C2H6 used in the previous example, with the ‘mid-wave infrared’ (MWIR) and ‘long-wave infrared’ (LWIR) imaging spectral regions marked. Thermal imaging is primarily restricted to these regions, as these areas provide at least some good spectral regions in which atmospheric gasses (primarily, water vapor) can be avoided*. This gas spectral data assumes an 8% mol fraction (each) of CO2 and H2O with 1% mol fraction of C2H6, with the mixture at a temperature of 1200 K at 1 atm pressure, and pathlength of 1 cm.

The spectral data for this mixture is taken to be representative of that seen (for these species) in a typical solid fuel combustion problem. Examination of Figure 57 shows several spectral regions in which thermal imaging of the fuel surface could be carried out without interference from the gas-phase emissions, assuming no soot is present. In the

MWIR range, an effective region lies between about 3.7 μm to 3.9 μm (the data in this figure appears to suggest a wider usable range in this region, but emissions from hydrocarbons larger than those which could be modeled here restrict the clear spectral region to the stated values). In the LWIR range, a useful spectral region for radiometric thermal imaging lies between about 8.25 μm to about 10.62 μm. In these regions, attenuation (for the stated gas mixture and conditions) is no greater than about 0.4%, allowing the capture of radiation from the fuel surface without attenuation in the gas phase, or reflection from the gas off of the surface.

* Development of thermal imaging sensors has been primarily driven by military and surveillance applications, which require very long imaging path lengths. Accordingly, spectral regions of strong attenuation by atmospheric gasses have traditionally been avoided in detector design.

122 Conditions Broadband Narrowband MWIR Narrowband (2.50-24.93 μm) (3.70-3.95 μm) LWIR (8.25-10.62μm) Sample Area Planck # Density Temp ε τ ρ ε τ ρ ε τ ρ (mg/cm2) (K) 0 1.85 300 0.699 0.254 0.047 0.514 0.393 0.093 0.861 0.102 0.037 0 1.85 325 0.692 0.260 0.048 0.514 0.393 0.093 0.861 0.102 0.037 0 1.85 350 0.683 0.266 0.051 0.514 0.392 0.094 0.861 0.102 0.037 0 1.85 375 0.674 0.273 0.053 0.515 0.392 0.093 0.860 0.103 0.037 0 1.85 400 0.664 0.281 0.055 0.515 0.392 0.093 0.860 0.103 0.037 0 1.85 425 0.655 0.288 0.057 0.515 0.392 0.093 0.860 0.104 0.036 0 1.85 450 0.645 0.296 0.059 0.515 0.391 0.094 0.860 0.104 0.036 0 1.85 475 0.636 0.303 0.061 0.516 0.391 0.093 0.860 0.104 0.036 0 1.85 500 0.627 0.309 0.064 0.516 0.391 0.093 0.860 0.104 0.036 0 1.85 525 0.619 0.315 0.066 0.516 0.391 0.093 0.860 0.104 0.036 0 1.85 550 0.612 0.321 0.067 0.516 0.391 0.093 0.860 0.105 0.035 0 1.85 575 0.606 0.325 0.069 0.516 0.391 0.093 0.859 0.105 0.036 13 1.62 600 0.571 0.361 0.068 0.467 0.438 0.095 0.831 0.130 0.039 72 1.25 625 0.549 0.385 0.066 0.431 0.469 0.100 0.784 0.182 0.034 82 0.77 650 0.446 0.482 0.072 0.330 0.556 0.114 0.654 0.305 0.041 29 0.40 675 0.379 0.547 0.074 0.285 0.601 0.114 0.491 0.452 0.057 29 0.40 700 0.376 0.548 0.076 0.285 0.601 0.114 0.491 0.452 0.057 29 0.40 725 0.374 0.549 0.077 0.285 0.601 0.114 0.492 0.452 0.057 29 0.40 750 0.372 0.550 0.078 0.285 0.601 0.114 0.492 0.452 0.057

Table 10: Spectrally integrated, normal incidence radiative property values for KimWipes® for temperatures from 300 K to 750 K for broad band (across entire tested spectral region) and two narrow bands that correspond to regions of interest for thermal imaging applications.

Table 10 shows the results of integrating each of the radiative properties over the spectral data from the final data set in these narrow band regions, along with the broad band values for the entire spectral range for this study. The emittance data for each of these spectral bands are plotted in Figure 59 as a function of the Planck temperature used in the calculations. This data shows that the emittance values in the narrow ‘imaging bands’ for both the MWIR and the LWIR change significantly over the temperature range from ambient to 750 K, which is assumed to be the highest temperature at which any of the solid material exists, prior to complete vaporization.

123 Integrated Emittance vs Temperature Broadband (2.50-24.93 microns) 1.0 MWIR (3.70-3.95 microns) LWIR (8.25-10.62 microns) e

c 0.8 n a t t i

m 0.6 E

d e t 0.4 a r g e t 0.2 n I 0.0 300 400 500 600 700 800 Temperature (K)

Figure 59: Example of band-integrated emittance as a function of temperature for broad and narrow bands in the MWIR and LWIR regions.

Figure 59 also shows that the emittance values in both narrow band regions (3.70 to

3.95 μm for the MWIR, 8.25 to 10.62 μm for the LWIR) stays relatively constant until the sample reaches 575 K, while the broad band emittance experiences a steady decline, starting immediately from 300 K. All of the integrated regions show a sharp decline from

575 K to 675 K, after which all reach nearly steady values.

This behavior might at first be unexpected, since the virgin sample was used for all integrations for temperatures up through 575 K. However, the reason for the discrepancies between the behaviors of the different spectral bands is that the shifting peak of the Planck curve (as temperature increases) affects the different spectral integrations differently. The sensitivity to changes in the shape of the Planck curve

(discussed briefly in Sections 2.3 and 4.5, and in more detail in Appendix III) generally

124 increases as the spectral band of interest is increased; narrow spectral regions tend to be affected less by shifts in the peak of the Planck curve.

The sharp decline in emittance seen in all of the integrated curves from 575 K to 675 K occurs when noticeable charring takes place in the sample. The dramatic changes in this temperature region reflect the fact that these samples underwent significant changes during pyrolysis in mass and in chemical makeup. The fact that this is the temperature region where significant mass loss occurs was observed in the numerical data seen in

Figure 15, which was used as a guide to pick appropriate temperatures to integrate the spectral data from each area density. While the sample mass and chemical makeup was

Initial Value Final Value Amount Percent of ε of ε Change Change Broadband 0.699 0.372 0.234 53% (2.50-24.93 μm) MWIR 0.516 0.285 0.231 55% (3.70-3.95 μm) LWIR 0.859 0.492 0.367 57% (8.25-10.62 μm) Table 11: Change in emittance (from ambient temperature to 750 K) in broadband and narrow imaging bands. both altered by the pyrolysis process, the primary reason for the dramatic change in the integrated radiative properties was mass loss. This is illustrated in Table 11, which shows that while the magnitude in the reduction of the emittance was significantly more for the 8.25 to 20.62 μm region (LWIR) than for either the broad band region or the narrow MWIR region (3.70 to 3.95 μm), the percentage change (when normalized by the band value at a temperature of 575 K) is comparable for all three spectral bands. This

125 indicates that mass loss is the primary mechanism for the change, with chemical changes accounting for smaller differences.

4.5.6 Estimation of Temperature Errors if Incorrect Emittance Values Used

The magnitude of error due to the use of incorrect emittance values in either thermal imaging measurements or numerical calculations can be estimated using the Stefan-

Boltzman law:

E T 4 Equation 9 where E is the total emissive power, εis the emittance, σis the Stefan-Boltzman constant, and T is the temperature in Kelvin. Since the emissive power is (in effect) the actual quantity measured by the thermal imager (temperature is determined using a calibrated ‘look-up’ table), the effect of using an incorrect emittance can be found by equating the actual temperature (raised to the fourth power) multiplied by the actual sample emittance to the indicated temperature (also raised to the fourth power) times the value of emittance that is assumed:

4 4 actualT actual assumedT indicated Equation 10

then solving for Tindicated, which is the approximate temperature that the imager will indicate. This temperature is an approximation because the Stefan-Boltzman law is an integrated form of the Planck equation, where the limits of integration range from zero to infinity (i.e., the entire electromagnetic spectrum). The thermal imager is assumed to be

126 Actual T=300 K Actual T=500 K Actual T=700 K Emittance Emittance Imaged in Imaged in Imaged in Imaged in Imaged in Imaged in Method Value MWIR LWIR MWIR LWIR MWIR LWIR

Blackbody 1 254 K 289 K 424 K 482 K 511 K 586 K

Gray (text value) 0.9 261 K 297 K 435 K 494 K 525 K 602 K Broadband Integrated Variable 278 K 316 K 476 K 541 K 653 K 748 K MWIR band integrated Variable 300 K n/a 500 K n/a 700 K n/a Ave MWIR band value 0.4 320 K n/a 533 K n/a 643 K n/a LWIR band integrated Variable n/a 300 K n/a 500 K n/a 700 K Ave LWIR band value 0.68 n/a 319 K n/a 531 K n/a 646 K

Table 12: Temperatures that would be would be measured using both a MWIR and a LWIR camera, using emittance values obtained from different methods. The “n/a” (‘not applicable’) indicates that it would be inappropriate to use an imager of one spectral band with values that are clearly intended for use only in another band. This does not apply to the broadband integrated values, which might be thought to be applicable to either imaging band. using a spectral band-pass filter to limit its spectral range to the values appropriate for its type (either MWIR or LWIR), as determined in Section 4.5.3. Since the integration is no longer over all wavelengths, the functional dependence of temperature will be something different than fourth power, but the Stefan-Boltzman law serves (in this example) as a simple tool to estimate the error caused by using an incorrect emittance value*.

The data in Table 10 shows that for the MWIR data the normal incidence emittance values for KimWipes® vary from 0.516 to 0.285, while the LWIR band emittance values vary from 0.861 to 0.492. The temperatures that could be measured with an infrared camera using these values and using either a blackbody approximation or a constant gray

* Error also results from a variety of other factors such as calibration, detector performance, and signal processing errors as well as the fact that spectral filters generally do not cut off precisely at the stated wavelength, but pass a small amount of additional energy from nearby wavelengths (termed “roll-off” of the filter). Such issues are outside the scope of this work.

127 value in each band are shown in Table 12. Temperatures are also calculated using the median emittance value from the spectral integrations for the MWIR and LWIR bands.

This data shows that temperature errors of up to nearly 190 K could be measured if the incorrect emittance values were used (MWIR, at temperature of 700 K, if blackbody value used), which means that the use of constant value radiative properties for thermal imaging of burning fuels can lead to surprisingly large errors in temperature measurement. Further, the error itself is temperature dependent (often in unexpected ways), as shown by the fact that the temperature observed using a gray-value of ε=0.9 with a LWIR imager will be only 3 degrees low at a true temperature of 300 K, and 6 degrees low at a true temperature of 500 K, but will be 98 degrees under predicted at a true temperature of 700 K. The temperature error is even greater (in both MWIR and

LWIR) if ε=1 is used.

Applying a similar approach to the broad-band data allows an estimation of what effect the new results will have on the calculated surface temperature determined by a numerical combustion model. Figure 60 shows the calculated temperature as a function of the actual surface temperature, with the blue curve representing the ideal case of a completely accurate temperature calculation (within the limits of the assumptions of this work, the broad-band integrated data should allow a good approximation of this curve).

The red curve shows the results using a gray emittance approximation across the entire spectral range (this plot was developed by using the band-integrated data from this study, along with the ‘actual’ surface temperature and the gray value of ε= 0.90 in Equation

128 10). The difference between the two curves represents the temperature difference that would be calculated, based on the broad-band integrated results from this study.

Temperature Error Using Gray Approximation 800 Broadband Integration

e r u

t 700 a r e p

m 600 ) e K T ( d e

t 500 a

l Actual Temperature (K) u c l

a 400 Temperature Calculated with C ε= 0.90 300 300 400 500 600 700 800 Actual Tempearture (K)

Figure 60: Calculated temperature as a function of actual temperature for the case of gray emittance = 0.90. The deviation between the curves represents the error in calculated temperature caused by the gray approximation, based on the integrated spectral data.

This plot shows that the calculated temperature (using the gray approximation) appears to plateau between 600 and 650 K. The calculated temperature actually decreases slightly

(by about 7 K) over this range, due to the sharp drop in actual emittance that occurs as the area density decreases*. The result of this ‘plateau’ in calculated temperature is a rapid increase in error in the calculated surface temperature, with the error rising to about 150

K by the time the surface would reach a theoretical temperature of 750 K. This demonstrates the impact that the data developed in this study can have on the accuracy of

* As previously stated, the numerical model used to perform the band integrations did not employ either the radiative property results from this work, or the newly measured values of activation energy and pre- exponential factor that were determined by this study. While the addition of these improvements may alter the relationship of area density as a function of temperature which was needed to perform the band integrations, the general behavior discussed here will remain, as it is a manifestation of the dramatic decrease in area density as the sample is pyrolyzed.

129 the numerical models, as the changes in band-integrated data that are brought about by the changes in area density (as the fuel pyrolyzes) can now be quantified.

4.6 Determination of Activation Energy

The creation of the heat-treated samples for the spectral examination portion of this study provided an opportunity to experimentally determine values for the activation energy and pre-exponential factor used in the zeroth-order , which is sometimes used to model pyrolysis of thin solid fuels5,50. Comparison can then be made between the experimentally determined values and those values previously used in models.

Area Density vs. Heat Treatment Time

2.00E-03 ) 2 m

c 1.50E-03 / g (

y t i

s 1.00E-03

n 325598 CK (598 K) e

D 350623 C K (623 K)

a

e 5.00E-04 375648 C K (648 K) r

A 400673 C K (673 K) 0.00E+00 0 30 60 90 120 150 180 Heat Treatment Time (sec)

Figure 61: Area density as a function of heat treatment time for a variety of oven temperatures. The linear behavior of the data suggests a zeroth order pyrolysis model is valid for the tested conditions.

The area densities of samples from each of the selected temperatures were plotted as a function of time, shown in Figure 61. Linear curve fitting was applied to each data set,

130 and the quality of those curve fits was evaluated by determining the R2 coefficient for set*. The correlation coefficients ranged from approximately 93% to 97%. The linear behavior of the data suggests that, within the range of the acquired data, a zeroth-order mass loss model (as shown in Equation 11) is a reasonable representation:

E    k AeRT  Equation 11

In this expression, k is the burning rate, E is the activation energy, R is the universal gas constant, T is the temperature (in Kelvin), and A is the pre-exponential factor. In this experiment, the measured mass loss rate at a given temperature (i.e., the slope of the curve fitted data) is used as the burning rate.

Activation Energy Curve for KimWipes

E= 33.9 kcal/mol/K -9.0 A=3.35*107 cm/s -10.0 y = -17038x + 15.991 R2 = 0.9773 -11.0 k

n -12.0 l -13.0

-14.0

-15.0 1.45E-03 1.55E-03 1.65E-03 1.75E-03 1/T (K-1)

Figure 62: Natural log of the burning rate ‘k’ versus 1/T. The burning rate data for this plot was taken as the slope of the mass loss vs. time data for each heat treatment temperature.

* The R2 coefficient is a measure of how much of a change in the independent variable is due to a change in the dependent variable in a given data set. This coefficient is computed as the proportion of the sum of the least squares of deviations of the independent variable values about their predicted values that can be attributed to a linear relationship between the dependent and independent variables48.

131 Figure 62 shows the natural log of k plotted against 1/T. After linear curve fitting, the slope of this line is equal to E/R. Using a value of R=1.989 cal/mol/K, the activation energy E is found to be 33.9 kcal/mol/K. The pre-exponential factor A is found by exponentiating the y-intercept of the curve fit. Using the value for the density of

KimWipes® that was previously used in a numerical model5,50 of 0.263 g/cm3, the pre- exponential factor was calculated to be 3.35x107 cm/sec.

Pre-Exponential Activation Factor Energy Previous 3.8 x 107 cm/sec 30 kcal/mol/K Values5

New Values 3.35 x 107 cm/sec 33.9 kcal/mol/K

Percentage -11% +13% Change

Table 13: Calculated values of the pre-exponential factor (A) and the activation energy (E) found using the current experimental data, as well as previously used values5 of the same quantities.

Table 13 presents these values, as well as the corresponding values used by Ferkul, Jiang and others in numerical models5,21,50, and the percentage difference from the old values to those calculated here. This table shows that the pre-exponential factor and the activation energy varied by similar percentages, but in opposite directions, with the activation energy increasing by 13% and the pre-exponential factor decreasing by about 12%.

132 While a full study of how these changes will affect the numerical results is beyond the scope of this effort, some insight can be gained by examining the burning rate as a function of temperature as calculated using both the old and new values of E and A.

Figure 62 demonstrates this, with the blue curve showing k(T) calculated with the previously used values, and the red curve showing k(T) with the experimentally determined results.

Qualitatively, both curves show similar behavior. Both show the burning rate to be very low at low temperatures, then accelerating sharply at higher (but different) temperature.

From a practical standpoint, the nearly vertical slope of the burning rate curve represents a limiting value that indicates sample burnout. Using the old values of A and E, the burning rate begins to accelerate at around 530 K, and has reached a value of 0.001 g/cm2/s by about 615 K. When the new values of A and E are used, the burning rate

Burning Rates for KimWipes Using Old & New Activation Energy & Pre-exponential

0.0010 Previously used A, E ) c

e New Values of A, E s /

2 0.0008

m Old Values: c / 7

g A=3.8x10 cm/s (

' 0.0006 E=30000 cal/mol/K k '

e t a 0.0004 New Values:

R 'Burning Rate' 7 g A=3.35x10 cm/s calculated using n i 0.0002 th n E=33889 cal/mol/K

r zero order law u B 0.0000 300 400 500 600 700 800

Temperature (K)

Figure 63: Calculated burning rates for KimWipes using both previous and newly calculated values of the activation energy and pre-exponential factor. The new values suggest a significantly higher peak surface temperature, which is closer to experimentally seen surface temperature values.

133 doesn’t begin its sharp acceleration until about 590 K, and reaches the value of 0.001 g/cm2/s at about 705 K.

Figure 64: Experimental thermocouple data traces49 showing surface and gas temperature profiles for KimWipes® burning in 18% O2, 10 cm/sec concurrent flow, in microgravity.

These values take on greater significance when compared to actual surface thermocouple test data49. This thermocouple data (shown in Figure 64) gives a peak surface temperature of about 725 K just prior to burnout. That value is much closer to the surface temperature estimated when using the newly acquired values of A and E, than with the previous values.

134 5.0 Summary & Conclusions

5.1 Summary of Experimental Results

The accuracy of the surface radiation model in numerical calculations of solid fuel combustion problems is compromised by the lack of detailed knowledge of the radiative properties of the fuel, and how those properties change with wavelength, incidence angle, fuel temperature, and area density (or, thickness). This study provided insight into how these variables affect the radiative properties of KimWipes®, a common thin fuel used in combustion studies. The spectral data gathered in this study also enabled band integrated information to be determined, for use in overall heat transfer and thermal imaging applications.

The experiment was performed by producing a series of progressively charred

KimWipes® samples which were deemed to be representative of samples that undergo combustion. These samples were created by heat-treating them in a constant temperature oven for varying times. The choice of oven temperatures was guided by data from a numerical combustion model, which indicated the temperature range over which the majority of pyrolysis effects are expected to occur*. An extensive sample set with different thermal histories was developed to allow determination of whether the samples’ thermal history would affect the spectral radiative property values.

* Note, however, that the model used to guide the selection of oven temperatures did not employ the values of A (pre-exponential factor) and E (activation energy) that were later determined.

135 The spectrally resolved radiative properties for KimWipes® were determined using an

FTIR spectrometer, along with an integrating sphere. Measurements were made in several novel configurations that allowed measurement of the property values at different incidence angles, as well as estimation of the degree to which transmitted light is scattered off axis. These measurements show the importance of ‘forward scattering’ in thin fuels. Failure to account for forward scattering can lead to considerable error in the absorptance when only (undeflected) transmittance and reflectance are measured.

Further, this ‘forward scattering’ behavior implies that for a thin fuel, even the very long path length that could theoretically be found at very steep incidence angles would not lead to 100% absorption, as some of the energy would be scattered off the straight line transmission axis, and therefore lost out of the sides of the thin fuel.

Overall, the angular dependence of the radiative properties was found to be mild until incidence angles of 45o or greater. Somewhat more absorptance was observed at incidence angles of 45o and 60o, primarily attributed to increases in the pathlength as the angle increased. Incidence angles of greater than 60o could not be tested in the integrating sphere used in this study, due to spatial constraints. Reflectance was found to be fairly low, even at the steepest angles that could be tested. This result was expected, due to the fibrous, non-homogenous nature of the material surface.

Samples with similar area densities but different heat treatment temperatures and times were compared, to determine if thermal history affects the spectral signature of the sample material. Five different comparisons were made at different area densities for

136 normal incidence, and several additional comparisons were made at different incidence angles. Small differences were detected in some cases (generally, only in narrow spectral regions), but most differences were within experimental uncertainty.

Further, comparison was made between multiple sheets of virgin KimWipes® and a single sheet of virgin Ashless Filter Paper, another thin fuel sometimes used in combustion studies. Ashless Filter Paper has an area density approximately four times that of KimWipes®, and has a considerably different fiber structure. The spectral data showed that the signature for Ashless Filter Paper is qualitatively similar to that of

KimWipes®, and is quantitatively very similar to four sheets of KimWipes®. Because of the overall similarity between samples of similar area density (regardless of heat- treatment history), as well as the similarity between four sheets of KimWipes® compared to one sheet of Ashless Filter Paper, the spectral property values were determined to be a function only of area density (within the limits of resolution of this study). This meant that the radiative property values were found to be independent of thermal history, and a much smaller sample set could be used to represent the behavior of the material. This has significant implications for the application of this data to numerical combustion models, since correlation with area density can be easily implemented.

Comparison was made between the heat-treated samples created in this study and a combustion sample that was made by burning a sample in concurrent flow in a near limit case, and lowering the pressure while the sample was burning to a a level below the flammability limit, in order to quench the sample. While this sample was not as uniform

137 in appearance as the heat-treated samples, its spectral signature was found to closely match a heat-treated sample of similar area density. Although obtaining combustion samples proved impractical as a sample manufacturing technique, the limited comparison still provided strong evidence of the validity of the area density correlation.

Measurements were made of the void fraction that was observed as a result of the fiber structure of the KimWipes®, both for the virgin material and for the heat-treated samples.

The size of even the smallest voids that could be measured were large enough (compared to the wavelengths measured in this study) that these voids could be expected to allow a significant fraction of the incoming light to pass directly through the material. The void fraction was seen to drop slightly as the material was initially subjected to heat-treatment.

This shrinkage in void fraction was attributed to contraction of the fibers as they were heated, causing the material to shrink slightly. However, the void fraction was observed to rise considerably as the sample pyrolyzed, with about three times the void fraction evident in the most charred samples, compared to the virgin material.

The spectral variation in the radiative properties was examined as a function of area density. All samples exhibited considerable spectral dependence. Variations with respect to area density followed the expected trends, with less dense samples transmitting significantly more light than higher density samples. Heat-treated samples showed small differences from the virgin samples in certain spectral regions, but over most of the spectral range, little difference was seen between samples of similar area density that were heat-treated in different ways. The one region where significant differences were

138 noted between heat-treatment times was in the carbonyl band (5.7 to 5.9 m). This was shown to be a narrow region in which the temperature history affects the spectral results.

Integrations of the spectral data were performed over temperatures from ambient up to

750 K. The broad band integrated data showed significant variation with temperature, with values of normal incidence emittance varying from 0.699 (for virgin material) in ambient temperature to 0.372 (for severely charred material) at 750 K, when using area density and temperature information from a previous numerical model. The entire spectral range of the data (2.50 to 24.93 μm) was also integrated at a variety of temperatures (for each char condition) to permit development of proper correlations for all tested incidence angles, for use in numerical combustion models.

Additional spectral integrations were performed for narrow band regions where thermal imaging would be useful as a diagnostic for concurrent flow combustion experiments.

These bands were determined by examining the transmittance of gas mixtures with constituents and temperatures that are representative of those observed in combustion tests. The spectral data for the gas mixtures was obtained using the HITEMP data base.

Bands of 3.70 to 3.95 μm (MWIR) and 8.25 to 10.62 μm (LWIR) were identified as appropriate bands for thermal imaging in concurrent flow conditions, since these bands exhibit virtually no emissions from CO2,H2O, and most hydrocarbons. The emittance of the MWIR imaging band was found to vary with temperature from 0.516 at room temperature to 0.285 at 750 K, while the emittance in the LWIR band varied from 0.859 at ambient to 0.492 at 750 K.

139 While the magnitude of the variations was different in each of the three integrated regions, the percentage variation from initial to final value was similar for each case, which again is suggestive that the majority of variation is due to reduction in area density.

Examination of how the emittance in each integrated band varied with temperature showed that significant variation in the integrated property values is due to the shift in the peak of the Planck curve with increasing temperatures, which gives temperature dependence to the importance of spectral features. This means that as the temperature changes, spectral features become more or less important to the integration at that temperature. This effect becomes more pronounced as the spectral limits of integration are widened, while narrow bands can be affected much less. This was demonstrated by the temperature dependence of the broad band integration for temperatures up to 575 K, since the same (virgin) sample was used to provide spectral data for all temperatures up to that point. The broad band integration showed a drop of about 10% in emittance over that range, while both narrow bands showed only about 1% decline in emittance over that same temperature range.

Estimation was made of the magnitude of the error in temperature measurement that could be made if a constant value of emittance were used in either heat transfer calculations or in radiometric thermal imaging. Temperature calculations were made for three ‘actual’ surface temperatures, with indicated temperatures governed by the different emittance formulations. Multiple variations of constant value emittance were used,

140 including blackbody, a typical constant gray value listed in textbooks, and the median of the variable emittance (in two separate bands) found in this study. Estimate of temperature errors from these constant value methods ranged as high as about 190 K (i.e., temperature difference from actual temperature), demonstrating the need to properly account for the changing emittance, both in narrow spectral band imaging applications and macroscopic (broad-band) heat transfer calculations.

The previously mentioned HITEMP data base was also used to examine a simplified example of the radiative coupling between the surface and the gas phase, simulating the situation in concurrent flow combustion. The data from HITEMP was used to model the radiative flux that could be seen under six different conditions, to evaluate what the absorptance of the surface would be under those conditions. In each case, the broad band absorptance of the surface was less than its emittance, though the difference in absorptance from condition to condition was relatively small, showing that while the band integrated absorptance is generally less than the band integrated emittance, it is not strongly affected by moderate changes in gas phase constituents (though soot was not modeled in any of the cases). In general, the band integrated surface emittance is a function of the spectral property values of the surface, its area density, and its temperature. The band integrated absorptance for the solid is not only a function of the properties of the solid, but also of the spectral nature and temperature of the gas-phase radiating source. This non-equality between the band integrated emittance and band integrated absorptance is not a violation of Kirchoff’s Law, but does serve to illustrate the need to apply the limitations of Kirchoff’s Law properly.

141 The large sample set that was originally developed to determine the dependency of the radiative properties on their thermal history also allowed determination of the material’s activation energy and pre-exponential factor within the framework of a zeroth order

Arrhenius pyrolysis model. This model was shown to be reasonable by the linear reduction in area density as a function of time that the samples displayed in their constant temperature heat-treatment regimens. The activation energy was found to be 33.9 kcal/mo/K (13% more than previously used values), while the pre-exponential factor was found to be 3.35 x 107 cm/sec, which is 11% less than previously thought5,21.

Using these new values, the pyrolysis rate for KimWipes® was calculated as s function of temperature, and the limiting value for the temperature (assumed to correspond to the burnout temperature) was found to be approximately 705 K, compared to 615 K using the previous values. This new value of 705 K compares favorably with experimentally measured peak surface temperature values of around 725 K, suggesting that the new values more closely simulate the pyrolysis rate than the previously used values.

5.2 Concluding Remarks

An important assumption to this work is that the spectral data would not be different if the sample were examined at elevated temperatures. This work showed that the spectral results at any given incidence angle (when pyrolyzed samples were examined at room temperature) were predominantly unaffected by the material’s thermal history, and were

142 then only a function of the area density of the material. While this certainly captures at least some of the effects that elevated temperatures have on the sample, final and definitive statements on how the temperature affects the spectral properties can only be made when information is available on how elevated temperatures would intrinsically affect the spectral values at any given pyrolysis state. If the effects of elevated temperature on the spectral data are small relative to the effects of changes in area density, then this work is a good representation of how changes in temperature (as manifested primarily by the pyrolytic mass loss) affect the spectral and band-integrated data. Even if elevated temperatures are later found to play a role in the spectral data, the effects measured and quantified here still capture a significant portion of the overall changes. The quantification of how temperature directly affects the spectral properties of a material in a given state of pyrolysis is left for future work.

The best possible measurement of the radiative property values of a burning surface would be direct, in-situ measurements, which would then account for all temperature affects (i.e., both pyrolytic effects and intrinsic temperature effects). Such a measurement would then capture all effects, and would allow separation of the temperature effects on the spectral data from the effects caused by mass loss, when taken in conjunction with the results from this work. However, since in-situ measurements of those properties are not practical (at least at the present), the methods and results from this study provide a practical and useful alternative, which were shown to give more accurate data than any other method to this date.

143 While the results of this work can be of immediate use for numerical combustion modelers who use thin cellulosic materials as their fuel source, a significant benefit of this work is that a methodology has been established for the determination of how the radiative properties of other thin solid fuels vary with respect to wavelength, incidence angle, and area density. A direct, useful by-product of that effort is that emittance values for use in thermal imaging diagnostics become available, making accurate, non-contact surface temperature measurements practical for the first time in solid fuel combustion experiments.

Further, the heat-treatment methods needed to create the samples also allow straight- forward determination of the activation energy and pre-exponential factors needed for the zeroth order pyrolysis model, and validated the usage of that model. The combination of the improvements to accuracy of the heat-transfer calculations (through the newly learned radiative properties) and the measurements of the needed constants for the pyrolysis model could affect the calculated flame structure and extinction limits, and should allow more accurate numerical combustion models which better reflect actual conditions.

144 6.0 Appendix I: Basic Principles of FTIR Spectroscopy

Spectral information on the fuel samples for this work was acquired using Fourier

Transform Infrared (FTIR) spectroscopy. Most FTIR spectrometers provide this information by measuring either the reflectance or transmittance of an object, typically using a Michelson interferometer. The following is intended only as a brief review of this topic, to illuminate the measurements and results of this work for the reader who is un-familiar with spectroscopy. Many texts are available which describe FTIR spectroscopy in significantly greater detail45,46,47.

6.1 Overview

Spectroscopy is the study of the interaction of electromagnetic radiation (or ‘light’) with matter. These interactions can take many forms, including emission, absorption, transmission, reflection, refraction, and a variety of modes of excitation. Examination of these processes often entails studying the spectral nature of light, which can be used to characterize the material that was interacting with that light.

Generally, spectroscopy is performed in one of two ways. The first type can be referred to as dispersive spectroscopy, in which radiation has been dispersed into its spectral components by an optical element (such as a prism or diffraction grating) either prior to or after being transmitted through or reflected off of a sample. The other method is interferometry, a technique in which spectral information is gathered by examining

145 interference patterns formed in light, rather than dispersing the light beam into spectral components.

The FTIR device used in this study employs a “Michelson” interferometer (a conceptually similar instrument was used by Michelson and Morley in their famous experiment), which is a device that splits a light beam into two components, then re- combines them at a later time, after a difference in their path length has been added by means of a moving mirror. This re-constituted light beam will now form an interference pattern, since a relative phase shift between the two beams (caused by the difference in path length) will result in a varying pattern of constructive and destructive interference, as a function of both mirror displacement and wavelength of light. This interference pattern varies in intensity with the difference in path length of the split beams, and is measured by a single element detector. The sample may be placed into the light beam either before or after the interferometer. This sample then selectively (based on its spectral properties, which is what is being measured) allows light to either pass through or be reflected off itself, depending on the instrument configuration.

The output of the instrument is called an interferogram, which is an interference pattern of those wavelengths of light that were transmitted (or reflected) by the sample. This interferogram is converted from spatial frequencies to spectral frequencies by performing a Fourier Transform on it (hence the designation ‘Fourier Transform Infrared

Spectroscopy’).

146 FTIR instruments can operate over a broad spectral region, limited by the spectral output of the light source, the spectral response of the detector, the transmittance of the interferometer and the travel distance of the moving mirror. The FTIR instrument used in this study provided usable data between approximately 400-4000 cm-1 (2.5 μm ~ 25 μm).

6.2 Advantages of FTIR vs. Dispersive Spectroscopic Techniques

FTIR spectroscopy offers several major advantages over dispersive spectroscopic methods. The first of these arises from the fact that interferometry allows spectral data at all wavelengths to be gathered simultaneously. This allows many scans (which contain all of the spectral data) to be averaged in a fairly short time compared to a dispersive technique, in which data at each discrete wavelength must be measured individually.

Averaging repeated scans is an effective way to improve the signal to noise ratio (SNR) of the measurement, but since improvement in the SNR from data averaging is proportionate to the square root of the number scans, a very large number of scans must be averaged to provide significant improvement.

As an example of this, consider the hypothetical case where a resolution of 600 discrete wavelengths was desired over a given spectral range. Further, assume that a dispersive technique would take 5 minutes to complete one collection of each of those 600 wavelengths at a data acquisition rate of two data points per second. Improving the SNR by a factor of three for this data set would require averaging nine data points at each wavelength, resulting in a total scan time of 45 minutes.

147 However, if the same 45 minutes used in this example were used to acquire data with an

FTIR instrument, about 2000 scans could be made (conservatively), each of which would contain all of the spectral data contained in the dispersive technique. By averaging 2000 scans, the SNR would be improved by a factor of about 45 (i.e., √2000), as opposed to the improvement factor of 3 seen with the same data acquisition time using the dispersive technique. This effect was first noted by P. Fellget in 1958, and has been known as

“Fellget’s Advantage” since that time.

The second significant advantage that FTIR provides over dispersive methods is in energy throughput. Known as “Jacquinot’s Advantage”, this advantage arises from the fact that dispersive techniques, by their nature, are spreading the available energy of the data-bearing light beam over a large number of wavelengths, each of which are measured separately. For example, measuring 500 independent wavelengths with a dispersive method would mean that the intensity at the detector (for each of the wavelengths) would be 1/500th of the intensity of the original beam (with some simplifying assumptions, for the sake of the example), without even accounting for any attenuation or scattering from the sample. By contrast, the FTIR instrument would have 100% of the original beam

(also neglecting attenuation from the sample) at the zero-retardation point, and significant fractions of the beam at other mirror positions. This means that the SNR of the measurement at each of these points will inherently be much lower than that of a measurement made with an FTIR, where the light beam is not separated into spectral components.

148 6.3 Basic Principles of the Michelson Interferometer

Michelson interferometers split an incoming beam of light into two beams using a beam splitter, each of which is approximately equal in intensity (monochromatic light beam of wavelength λ is considered first for simplicity; the discussion will then be extended to polychromatic light). One of these beams is reflected off of a stationary mirror, while the other is reflected off of a moving mirror, creating a pathlength difference between the beams. The beams are then recombined at the beam splitter and directed through (or reflected off of) the sample, and are then captured by a detector. Figure 65 shows the schematic layout of such an interferometer.

δ, μm

Figure 65: Schematic layout of Michelson interferometer.

149 The motion of the moving mirror creates a pathlength difference (referred to as the

‘retardation’, δ) which creates an interference pattern. This is observed as a temporally alternating pattern of high and low intensity at the detector, corresponding to the spatially varying interference pattern. When the two mirrors are exactly the same distance from the beam splitter (i.e., δ=0), the combined beam will be exactly in phase and constructive interference will produce a maximum intensity at the detector.

When the moving mirror is displaced a distance of ¼ λ, the retardation is ½ λ (the total change in pathlength is the distance the light travels both to and from the moving mirror).

At this retardation, the two beams are now totally out of phase, giving completely destructive interference, and zero intensity at the detector. If the moving mirror is allowed to continue moving in the same direction, its displacement will reach ½ λ

(retardation of λ) and constructive interference will cause a maximum intensity at the detector.

If the mirror is moved at a constant velocity, the intensity measured by the detector can be expressed as a function of the retardation, I=I(δ). The intensity will be a maximum at values of δ=nλ, where n is an integer value. In general, the intensity can be expressed as:

I() 0.5I (){1cos2} Equation 12

150 where νis the frequency expressed as wavenumber (ν= 1/λ) of the original light beam, and I(ν) is the intensity of that beam after passing through the interferometer.

The constant portion of this expression (0.5 I(ν)) is discarded, for the purposes of this discussion, and the remainder describes the varying intensity as a function of the retardation, also referred to as an interferogram. With a correction factor H(ν) added in to account for characteristics such as beam splitter efficiency, detector response, etc., the equation of the interferogram takes the form:

I() 0.5H()I()cos 2 Equation 13

This can be simplified by combining H(ν), I(ν) and the constant 0.5 into one term:

I () B() cos2 Equation 14

The spectrum is calculated by taking the Fourier transform of I(δ). When applied to the infrared portion of the spectrum, the name of the technique, “Fourier Transform Infrared spectroscopy” (FTIR) becomes apparent.

When the incoming light source is polychromatic, the interferogram is the sum of the intensities from all the wavenumbers. For the limiting case of all wavenumbers, this takes the form of the integral:

151  I () B()cos 2d Equation 15 

Since this is an even function, the Fourier Transform of this function can be expressed as:

 B() 2 I () cos2d Equation 16 0

This equation describes the spectrum observed when a polychromatic light source is used with such a spectrometer.

Examination of this equation suggests that (theoretically) the entire spectrum (i.e., wavenumbers from zero to infinity) could be measured at infinitely high resolution.

However, this would require the moving mirror to move from zero to infinity in terms of the retardation, which is physically impossible. Further, the data spacing, i.e., the change in retardation (dδ) needs to be infinitely small according to the integral.

From a practical viewpoint, there will be finite limits on both the travel range of the moving mirror and on the digital sampling rate of the data acquisition system of the FTIR device. These limitations, as well as performance limits of the light source and detector, will impose restrictions on both the spectral range and resolution of the device. The detector being used will place limits on the spectral range being studied, as the detector must be capable of responding to energy of the given wavelength (similarly, the ‘light’ source must be capable of supplying energy in the desired spectral range). The total

152 travel of the mirror must then be sufficient to capture the spectral range of the source and detector. The resolution of the interferometer will be a function of the ability of the system to resolve small changes in the position of the mirror.

153 7.0 Appendix II: FTIR Instrument Optimization Procedures and Settings

Optimized settings and procedures were determined for the FTIR spectrometer used in this study by means of testing in a variety of sample configurations. Various parameters were adjusted until the resulting data converged on the best resolution attainable, or until the data matched known results. The final settings and parameters used are listed in

Table 14 and discussed in this appendix.

Variable Tradeoff Optimization Method Optimized Setting

Light ‘leaks’ (back Entrance port through port) vs. 9 mm aperture opening higher signal input Reduce aperture until incoming signal drops below usable level Collimation of light vs. Bench setting of 100 Bench aperture greater signal (scale 0-150)

Spectral resolution vs. Increase resolution until Bench Resolution Data collection at 8 cm-1 data collection time spectra does not change

More scans take more Inspection of spectra at Number of scans to time, but allow better different number of 250 scans be averaged S/N ratio scans Spectral range cutoff Greater data range vs. Spectral collection when magnitude of -1 quality of spectra at 401 to 4000 cm range noise in edges increased 2.50 to 24.93 μmλ edge of range by factor of ~3

Position & angle of Incorrect spectral data Aligned optically wedge mirror

Table 14: Instrument and integrating sphere parameters with optimization tradeoffs, optimization method and optimized results.

154 7.1 Entrance Port

The optimization of the entrance port of the integrating sphere involved the tradeoff of minimizing the size of the port to reduce the amount of light that could potentially escape the sphere after internal reflections, versus maximizing the incoming beam size (by increasing the port diameter) to increase the incoming energy, and thereby increase the signal to noise ratio. Minimizing the light losses was rated the more important of the two considerations, so the optimization was reached by decreasing the entrance aperture until the observed interferogram had a peak-to-peak value of approximately 3 units (diagnostic parameter on the FTIR bench), which was deemed the minimum signal level that would yield good results. This result was verified by examining a series of spectra, and evaluating the relative noise levels in the signal. The entrance port diameter was controlled by attaching aperture plates (provided by manufacturer of sphere) to the entrance aperture of the sphere. Once this optimization was completed, this plate was used for all tests.

7.2 Integrating Sphere

The bench aperture is the aperture on the FTIR instrument from which the light beam exits, prior to entering the integrating sphere through the entrance port. Since this aperture is located upstream (in terms of the direction of the incoming light beam) of the entrance port, it will act to control the collimation of the beam by blocking the outermost portions of the beam. Since the beam focuses down to a minimum spot size (which

155 occurs inside the sphere, after the beam reflects off of the turning mirror), the outermost portions of the beam are at the largest angle, relative to the center portion of the beam.

Therefore, although stopping down the bench aperture will act to limit the amount of light that can reach the entrance aperture, the light that does reach the aperture will be more collimated. However, stopping down this aperture too much will reduce the incoming light signal, so the bench aperture was adjusted down (with the entrance aperture to the sphere in place) until the peak signal in the interferogram just began to reduce. The bench aperture was controlled through the FTIR instrument software, which gave the aperture settings in terms of dimensionless numbers ranging from 0 to 150. The setting used as the optimized value was 100. This value was used for all data acquisition.

The tradeoff regarding the bench resolution was that increasing the bench resolution requires more time per scan (since the moving mirror moves a greater distance, thereby allowing more data points to be taken over the total length of travel) but, increasing the resolution past the limit where all spectral peaks adequately represent the actual sample spectrum simply increases the data acquisition time without adding any useful information.

The bench resolution was optimized by starting at a relatively ‘coarse’ resolution, and then acquiring data at progressively greater resolution until no further spectral changes were observed. The resolution setting (on the FTIR instrument) at which this occurred was 16 cm-1, which corresponds to data spacing of 8 cm-1*. Greater resolution settings

* The Nyquist criteria requires sampling at no less than 8 cm-1 to resolve spectral features of spectral width 16 cm-1.

156 than 16 cm-1 caused no further spectral features to be detected in the sample material

(KimWipes®) used in this study.

The number of scans to be acquired and averaged was chosen to be 250 scans. This increased the signal to nose ratio (S/N) by a factor of 15.8, compared to a single scan.

This value was chosen by examining data acquired by averaging progressively more scans, and selecting a value which allowed resolution of small spectral variations in the data, while still acquiring data at a practical rate. Acquiring 250 scans per test required about 10 minutes of acquisition time per test, which was an acceptable amount of time per scan and still allowed for a useful data set.

The spectral range of data collected initially ranged from 400 to 8000 cm-1**. However, the noise levels evident at wavenumbers greater than 4000 cm-1 increased dramatically, with noise levels at 4000 cm-1 of approximately 3 times that seen at 2000 cm-1. Further, the magnitude of noise increase rapidly from that point as the wavenumber increased, so the data set was truncated at 4000 cm-1. The truncated range covered the wavelength range from 1.25 to 2.50 μm. Truncation of this range was judged to be acceptable, since

Wien’s Law shows that the peak experimentally measured temperature 49 of 725 K would cause a peak in the Planck function to occur at approximately 4 μm (Table 8 in

** Due to the inverse relationship between wavenumber and wavelength, differences between large wavenumbers correspond to small differences in wavelength, while the same span of wavenumbers taken between smaller wavenumbers correspond to large differences in wavelength. For example, the spectral range of 100 wavenumbers from 4000 to 4100 cm-1 represents a range of wavelengths from 2.44 to 2.50 μm (change of 0.56 μm), while the span of 100 wavenumbers between 400 to 500 cm-1 represent wavelengths from 20 to 25 μm (change of 5 μm).

157 Section 4.5 shows that the spectral range used in this study accounts for 91% of all possible energy at 725 K).

The placement of the wedge mirror (described in Section 3.2.1, used in all tests conducted inside the sphere) was determined visually to be located on the rear wall of the sphere, directly in line with the incoming light beam. This was verified by inserting the normal incidence sample holder that was used for ‘transmission + reflection’ measurements (i.e., with a hole in the center of the holder) into the sphere, and viewing the mirror alignment through the entrance port and the sample holder. When viewed at a distance, the entrance aperture and sample holder acted as an alignment assembly by allowing the viewer to insure that the viewing angle was similar to that of the incoming beam (when viewed at the proper angle, the edges of the sample holder could not be seen through the entrance aperture). By viewing at this angle, the wedge mirror was aligned so that it was centered where the beam would illuminate.

The tilt angle of the wedge mirror was set to be 5o (clockwise, when viewed from the entrance port), and was judged visibly to be such that no direct reflection would strike the detector. No uncertainty data is needed for this angle, as the mirror was tilted only to prevent reflections in one direction; no data depends on a quantitative value of this angle.

158 8.0 Appendix III: Effect of Planck Curve Shift on Band-Integrated Results

Since the shifting shape of the Planck curve (as the temperature changes) plays a role in determining the broad band integrated values of the radiative properties, a brief discussion of this effect is in order.

The peak of the Planck curve shifts to shorter wavelengths as temperature increases. This effect is summarized in the well-known Wien’s Displacement Law:

maxT 2897.8 m K Equation 17

which states that the wavelength of peak emissive power is inversely proportional to the temperature. The spectral shift of that peak can cause the band-integrated radiative property values to change, even if the spectral response of the material in question is unchanged. This shift in the spectral energy distribution in the Planck function causes the relative importance of the spectral features of the emittance to change, and can be demonstrated by applying the Planck curve at two different temperatures to the same set of spectral data, and comparing the integrated results.

That comparison was carried out using the normal incidence spectral absorptance data for virgin KimWipes® at normal incidence (Figure 28). Since the same spectral data is used, the only difference in integrated emittance can be through the differences in the Planck curves at different temperatures. The purpose of this comparison is merely to

159 demonstrate the effect of different temperatures in the Planck curve, not to suggest that using the virgin materials’ spectral data with such an elevated temperature is valid.

Spectral Emissive Power for Virgin KimWipes 50 1.00

40 Plank Function @ ) e 0.75

v 300 K m i s m e

* Emitted Power @ s 2 i 30 c 300 K (actual) n m m / a

E Spectral Emittance t l W

0.50 t ( i a r r t e 20 m c w E e o p Band Integrated P S 0.25 10 Emittance: 0.64

Integrated at 300 K 0 0.00 0 5 10 15 20 25 Wavelength (microns)

Figure 66: Spectral emissive power and spectral emittance of virgin KimWipes, integrated at Planck temperature of 300 K.

Figure 66 shows the results of using a temperature of 300 K in the Planck calculation, and applying it to the virgin KimWipes® spectral data, while Figure 67 shows a similar plot using a temperature of 750 K. The spectral emittance data for the material is plotted against the right axis (green trace) in both figures.

Using this data, the total emittance changes from a value of 0.62 when using a temperature of 300 K, to 0.44 when using 750 K. The reason for the change in total emittance can be seen by noting that, for the 300 K case, the large peak in emittance between 7 to 11 microns in the spectral data coincides with the peak in the Planck emissive power curve, at 10 microns. However, the 750 K case shows that a local

160 Spectral Emissive Power for KimWipes

5000 1.00

) Planck Function @ e 4000 v m i 0.75 750 K m s e

* Emitted Power @ s 2 i c 750 K (actual)

m 3000 n m / Spectral Emittance a E t W l

0.50 t ( i a r r t

e 2000 m c w E e o p 0.25 Band Integrated P S 1000 Emittance: 0.47

0 0.00 Integrated at 750 K 0 5 10 15 20 25 Wavelength (microns)

Figure 67: Spectral emissive power and spectral emittance of virgin KimWipes, integrated at Planck temperature of 750 K. minimum of the spectral emittance falls under a spectral region of high emission from the

Planck curve, since the peak of the curve has shifted towards 4 microns.

These results demonstrate that for any material whose radiative properties are spectral in nature, the total (band integrated) radiative property values will change as a function of temperature, regardless of whether the spectra changes. This effect will cause significant inaccuracy in heat transfer calculations in solid fuel combustion models if constant value, band-integrated emittance data is used, due to the large temperature range of the calculations and the spectral nature of virtually any fuel.

161 9.0 Appendix IV: Experimental Uncertainty Analysis

This appendix will characterize and, where appropriate quantify the experimental uncertainties that this work was subject to. Tables 15-18 list the uncertainties related to this experiment, broken down by classifications. The tables also summarize how the uncertainty was quantified or controlled, where in the data set the given uncertainty would appear, and the magnitude of the uncertainty in the data, if applicable. The general classifications include uncertainties in the samples and oven performance (Table 15), the area density measurements (Table 16), FTIR instrument performance and spectral measurements (Table 17), and activation energy determination (Table 18) for the collected data set, taking into account the sources of uncertainty in each of the measurements. The items in each of the tables are discussed individually.

9.1 Sample Reproducibility

Table 15 shows the uncertainties related to the reproducibility of the samples. The first three listed uncertainties relate to possible differences in the virgin samples from lot to lot, i.e., differences in the manufacturing process. These potential differences include variations in fiber structure, chemical makeup (i.e., additives), and area density.

These uncertainties were addressed by examining samples (spectroscopically) from multiple boxes, and acquiring area density data from those samples. No difference was detected in either area density or spectral signature from box to box, within experimental

162 resolution. Still, all data was collected using samples from a single box to prevent even small lot to lot variations.

Thermal gradients in the oven were considered and characterized by acquiring thermocouple (TC) data using a Type K thermocouple, mounted to the sample holder on the oven carriage (Figure 3). The thermocouple was mounted at varying locations on the sample holder, and inserted into the oven when the oven controller indicated that a stable temperature of 623 K was achieved. The thermocouple data (which itself has a manufacturers stated uncertainty of 2 K in absolute temperature) showed variations of no more than +/- 2 K.

The uncertainty in the absolute temperature of the oven is a combination of the uncertainty of the thermocouple, and of the gradient in the oven. This combination of uncertainties equates to a total uncertainty of 4 K in the oven’s temperature.

The duration of the heat-treatment process was measured using a digital watch, with precision to 0.01 sec. However, operator performance (in terms of small delays in starting or stopping the watch, co-ordinated with placement or removal of the sample) was estimated to have approximately 1 second in uncertainty. This uncertainty was essentially fixed, regardless of the intended duration of the heat-treatment process. This uncertainty was minimized by consistently using a rigid procedure in the sample handling process, as it related to the heat-treatment timing.

163 Sample Reproducibility Where Magnitude of Source of Uncertainty How Quantified or Controlled Uncertainty is Uncertainty in Data Evident Samples tested from multiple boxes Different fiber structure for common signature; same box Spectral data Negligible (lot to lot) used for test data Samples tested from multiple boxes Different chemical for common signature; same box Spectral data Negligible makeup/additives (lot to lot) used for test data

Different area density of virgin Multiple samples measured; same Area density, Negligible sample (lot to lot) box used for test data spectral signature

TC data acquired at different oven Temperature variations in oven positions; oven allowed time to Area density +/- 2 K equilibrate

Activation energy Temperature of oven TC manufacturer's specs +/- 4 K calculations

Heat-treatment timing Digital watch used to time duration Area density +/- 0.01 sec uncertainty

Heat-treatment sample Repeatable methods used Area density ~ +/- 1 sec handling uncertainty

Sample treatment: heat treated Comparison made between burned Spectral data, Negligible vs. burned and heat-treated samples area density

Table 15: Sample reproducibility and oven uncertainties.

One final area of possible uncertainty in sample reproducibility relates to the fact that heat-treated samples were used to simulate samples that would be produced in a true combustion procedure. This issue was addressed in Section 4.4.9, in which a comparison was made between several heat-treated samples and a sample produced in an actual combustion experiment. Results of that comparison demonstrated that the samples produced in both ways were nearly indistinguishable over most of the tested spectral region, with small deviations noted around 5.10 μm, corresponding to changes in the carbonyl band.

164 9.2 Area Density Measurements

The procedure used to measure the samples’ area density was described in Section 3.1.2.

Potential sources of uncertainty in these measurements include the precision, accuracy and repeatability of the samples (Table 15), human accuracy in cutting out the Xeroxed shape of the sample (used for determining the area of the irregularly shaped samples), and the precision, accuracy and repeatability of the balance used to weigh the samples

(Table 16). The issue of human accuracy in cutting the sample shapes was quantified by

Area Density Uncertainty Magnitude of Source of How Quantified or Where Uncertainty Uncertainty in Uncertainty Controlled is Evident Data

Error in cutting Multiple tests of same Area density +/- 0.82 mg out Xeroxed shape sample

Precision of Manufacturer Specs Area density 0.001 mg balance

Accuracy of Manufacturer Specs Area density 0.002 mg balance

Multiple samples Repeatability Area density +/- 0.01 mg weighed

Overall uncertainty in area density measurements 0.07 mg/cm2

Table 16: Area density measurement uncertainties. cutting out a given sample shape six times, and determining the standard deviation of the mass of those shapes to be 0.41 mg. Assuming a normal distribution, two standard deviations (2σ) signify the 95% confidence interval (+/- 0.82 mg), which is the value reported in Table 16.

165 The balance used to determine the mass measurements used for this work was verified to be within annual calibration, and a one point calibration was performed before each series of measurements. Manufacturer stated specifications for precision and accuracy were reported as +/-0.001 mg and +/-0.002 mg, respectively. Repeatability of the measurements was quantified by weighing a 5 mg reference weight six times, yielding a

95% confidence interval (2σ) reported in Table 16 to be +/- 0.01 mg.

9.3 FTIR Instrument Performance and Spectral Measurements

Table 17 shows the uncertainties related to the spectroscopic data, both in terms of the

FTIR instrument, and with regard to issues such as sample misalignment, and cracks and holes in the sample.

Uncertainty in the position of the moving mirror in the FTIR instrument is both minimized and characterized by an internal measurement (in the FTIR instrument) of the interference pattern of the HeNe laser light emission of 0.6328 μm. The instrument projects this light through the same path length difference used in the spectral measurements, though the detector used for the laser is located internal to the bench. The mid-point of the fringes from this interference pattern (i.e., the point where the sinusoidally varying pattern reaches zero) is observed twice per period of the interference. These points are used as reference (calibration) points, where the distance that the mirror has moved can be referenced to a known standard (one half the

166 wavelength of the HeNe laser line). By referencing the mirror’s position to these known points, the uncertainty in mirror position is virtually eliminated. The fact that the FTIR instrument can almost continuously calibrate itself with respect to wavelength is known as Canne’s Advantage, and allows extreme accuracy in terms of wavelength resolution.

For the mirror displacement required to achieve the data spacing of 8 cm-1 in these tests, more than four references (on average) were made to the laser fringes for each data point acquired. Due to this, uncertainty in the wavenumber (and therefore, the wavelength) is neglected.

The group of potential uncertainties that were associated with sample blanking (noted in

Table 17) was described in Section 3.3. These included the sphere aperture and bench aperture settings, light losses in the sphere, detector and light source performance, and the effects of multiple reflections in the sphere. The process of sample blanking inherently accounts for all of these issues and are therefore not a factor in the uncertainty of the spectral data.

167 FTIR Data Uncertainty Where Uncertainty is Magnitude of Source of Uncertainty How Quantified or Controlled Evident Uncertainty in Data Uncertainty in moving Reference to HeNe laser in FTIR Wavenumber resolution in Negligible mirror position instrument spectral data

Aperture/bench settings Repeatable settings used n/a n/a

Light losses in sphere Sample Blanking Spectral Data Negligible

Detector performance Sample Blanking Spectral Data Negligible

Light source Sample Blanking Spectral Data Negligible performance Unknown number of Sample Blanking Spectral Data Negligible reflection in sphere Uncertainty due to Use of repeatable procedures, Spectral Data Negligible sample misalignment visual inspection Uncertainty in sample Measurement of holder angle Angle for Spectral Data +/- 2 degrees mount angle Use of repeatable procedures, Cracks in samples Spectral Data Negligible visual inspection

Holes/voids in samples Imaging measurements Spectral Data Negligible

Repeatability of Spectral Spectra from repeated samples Spectral Data +/- 3 % Data Accuracy of Spectral Comparison of inside vs. outside Spectral Data +/- 5% Data sphere test Total Uncertainty in RSS method combining accuracy Spectral Data +/- 5.8% Spectral Data and repeatability Repeatability of Band Integration of repeated samples Integrated Data +/- 1% Integrations Accuracy of Band Comparison of inside vs. outside Integrated Data +/- 3% Integrations sphere test Total Uncertainty in RSS method combining accuracy Integrated Data +/- 3.2% Integrated Data and repeatability

Table 17: FTIR instrument and spectral data uncertainties. Several potential sources of uncertainties in the spectroscopic data could be attributed to the samples. These issues are listed here rather than in Section 9.1 because these are issues directly related to mounting the samples, or issues that will have a quantifiable

168 effect on the spectral data, while the issues listed in Section 9.1 related more to the manufacture of the samples, or to the heat-treatment process by which the samples were created. The uncertainties regarding samples that are relevant to this section include things such as sample misalignment on the sample holders, uncertainty in the angle of the sample holders relative to the incoming light beam, cracks or tears in the sample, and the presence of holes in the sample.

Sample misalignment on the sample holder could cause part of the tape (used to hold the sample to the sample holder) to be present in the direct light beam, which would add part of the tape’s spectral reflectance signature to the sample data. This was avoided procedurally, by repeatedly mounting the sample on the holder in a way to avoid having the tape in the light path. The proper mounting position was determined by visual inspection, and was verified by looking at each spectral data set for evidence of the spectral signature of the tape. The tape’s reflectance signature was determined by acquiring a spectrum in which the sample holder was intentionally covered with the tape.

The spectral reflectance of the tape has numerous unique, identifiable peaks that are unlike the spectral features seen in any of the cellulose samples, allowing for simple identification of any co-mingled spectral data. Any spectral data in which evidence of the tapes spectral signature was observed were simply discarded, and the data was re- acquired with the sample re-positioned properly.

Uncertainty in the sample holder angle was determined to be +/- 2 degrees, determined through direct measurement of the angle at which holder is bent.

169 Cracks and tears occurred in a few of the samples, particularly the highly fragile, heavily charred samples. Care was taken when handling and mounting the samples to minimize damage. Several times, damaged samples were discarded and data for all angles was re- acquired with the new sample. On the few occasions when no replacement sample of appropriate area density was available, care was taken to mount the sample with the tear or crack positioned so that no direct light path existed through the sample. The effectiveness of this method was verified by re-mounting a partially torn sample at an angle which that sample had previously been tested at, and verifying that the data produced by the torn sample matched that acquired at that angle before the damage. The effectiveness of this method leads to no quantifiable uncertainty in the final data.

The presence of holes (i.e., gaps between fibers) was demonstrated and investigated in

Section 4.4.8. The extent of holes in the sample was measured by imaging the samples on a gold slide with a microscopic lens and front lighting, then using computer software to threshold filter the images so that reflections from gaps between the fibers were set to high digital values, and the portion of the image corresponding to the fibers was set to low digital values. The software was then able to precisely count the number of pixels at both high and low values, allowing simple calculation of a volume fraction of voids by taking the ratio of high value pixels to total pixels.

The accuracy of the tallying of high value pixels can safely be assumed to be 100%, since this was performed on a computer. The only likely uncertainty associated with this

170 measurement would then be voids or gaps smaller than the imaging resolution, which would be neglected in the total void fraction. Each pixel was determined to represent

0.94 μm in the image, as determined by measuring the number of pixels covered by an object of known length. Since voids of this size were well below the shortest wavelengths measured in this study (2.50 μm), uncertainties due to underestimating the void fraction due to voids smaller than the imaging resolution are neglected.

The uncertainty in the repeatability of the spectrally resolved data was estimated by examination of multiple spectra of virgin KimWipes, as seen in Figure 68. The scatter in spectral data for these identical samples was found to be no more than +/- 3% for the spectral range. The uncertainty in repeatability of the band-integrated data was estimated by performing the integrations over this data, and was found to be +/- 1 %.

The absolute accuracy of the primary data (the data at all angles, acquired inside the sphere) can be estimated by comparison of the normal incidence transmittance data acquired inside the sphere versus the normal incidence transmittance data from the outside the sphere configuration. The data taken outside the sphere can be considered the more reliable of the two configurations, since it was taken in a configuration that was exactly what the integrating sphere was designed for, while the inside the sphere configuration was a custom configuration designed for the current effort. Therefore, if the data acquired outside the sphere is assumed to be accurate, then any deviations between the two data sets can be thought of as indicative of the relative accuracy of the data acquired inside the sphere.

171 Repeated Tests of Virgin KimWipes 100% Normal Incidence

75% e c n a t p

r 50% o s

b Test 1 A 25% Test 2 Test 3

0% 0 5 10 15 20 25 Wavelength (microns)

Figure 68: Normal incidence absorptance for repeated tests of virgin KimWipes®.

The comparison of the normal incidence transmittance data for virgin KimWipes® in both configurations was made in Section 4.1, with the results plotted in Figure 13.

Examination of this plot shows that the maximum deviation between the two data sets is generally within 3%, though small regions show a difference of 5%. The overall accuracy of the spectral data is then conservatively within +/- 5%. The uncertainties in the accuracy and repeatability were combined using the root sum of squares (RSS) method, to give a total uncertainty in the magnitude of the spectral data to be +/- 5.8%.

The band integrated data accuracy was evaluated by comparing the integrated data for these two cases, with agreement within 3%. The uncertainties with regard to accuracy and repeatability of the band integrated data were also combined using the RSS method to yield a total uncertainty in this data of +/- 3.2%.

172 9.4 Activation Energy Data

The activation energy and pre-exponential factor (according to a zeroth order Arrhenius law) were determined for KimWipes®, as described in Section 4.6. These calculations were based on the area density data acquired for the material, which could be plotted as a function of heat-treatment time at each of the four constant temperatures used to generate the samples.

Since the basis for these calculations was the pyrolysis rate (i.e., the rate in reduction of the area density as a function of heat-treatment time), estimation of the uncertainties of these values must be based on the uncertainties in the heat-treatment process, and on the uncertainties in the area density measurements.

Area Density vs. Heat Treatment Time 598 K 2.0E-032.00

) y = -0.00000389x + 0.00179325 2

m 1.8E-031.80 c

/ Area Density g Linear (Low Slope Error) m ( 1.6E-031.60 Linear (High Slope Error) y t i s

n 1.4E-031.40 e D

a

e 1.2E-03

r 1.20 y = -0.00000269x + 0.00168525 A 1.0E-031.00 0 30 60 90 120 150 180 Heat Treatment Time (sec)

Figure 69: Area density versus heat-treatment time, using maximum uncertainties in the area density measurements to determine the limiting range of slope.

173 Estimate was made of the effect that uncertainties in the area density had on the calculations by combining the possible uncertainties in area densities in such a way that the maximum changes in slope could be observed, as illustrated in Figure 69. The curve fit values from this data were then used in the calculations as described in Section 4.6.

Further, the uncertainty in temperature data was applied similarly in the calculations, to provide the maximum changes in slope in the plot of ln K as a function of 1/T.

The resulting high and low calculated values of the activation energy (E) and pre- exponential factor (A) obtained when using this approach are found in Table 18. These values represent the limiting case, when all uncertainties operate in such a way as to maximize the propagated error.

Pre-Exponential Factor Activation Energy Calculated Values 3.35 x 107 cm/sec 33.9 kcal/mol/K High Value 6.19 x 109 cm/sec 40.6 kcal/mol/K Low Value 6.79 x 105 cm/sec 28.9 kcal/mol/K

Table 18: Calculated values of E and A with uncertainty estimates developed using uncertainty estimates of area density measurements and heat-treatment temperature.

This same approach was used to evaluate the effect of using these uncertainty values to calculate the burning rate in order to estimate the peak temperature that would likely be observed in a combustion test. This approach was used to generate the data in Figure 63, in which the peak surface temperature (using the values of E and A found in this study) was estimated to be about 705 K. That data is re-plotted in Figure 70, along with the burning rates using the uncertainty estimates developed here. The peak surface temperatures predicted with the uncertainties (using the temperature observed at a

174 calculated burning rate of 0.001 g/cm2/sec) only deviate by about 10 degrees from those determined using the measured data.

Burning Rates for KimWipes Showing Uncertainty Propagation in E and A

0.0010 ) c e s

/ Previously used A, E 2 0.0008

m New Values of A, E c /

g High error bar (

0.0006 ' Low Error Bar k '

e t

a 0.0004

R 'Burning Rate'

g calculated using n i 0.0002 n th

r zero order law u B 0.0000 300 400 500 600 700 800

Temperature (K)

Figure 70: Predicted burning rate for KimWipes using uncertainties from area density and heat-treatment temperature, along with data generated using previous data and current data.

This data shows that despite the apparently large changes in the values due to the uncertainties in the area density and heat-treatment temperature, the combinations of activation energy and pre-exponential factor yielded by the propagation of these uncertainties still predict peak surface temperatures comparable to those values calculated with the measured data.

175 10.0 Appendix V: Complete Integrated Data Set

The spectral emittance data for the final data set was integrated across the entire tested spectral range of 2.50 to 24.93 µm for all tested incidence angles. These integrations were carried out at a variety of temperatures (in the Planck function), and are intended to be used to permit correlation as a function of area density in numerical combustion models.

This data set is presented in Table 19. The data shaded in blue was used for various comparisons throughout this work. The correlation between area density and temperature

(for use in the Planck function integration) was made using the previously discussed numerical model; that model calculated the area density as a function of temperature as shown in Figures 14 and 15. As previously noted, those modeling results did not employ the radiative property results gathered in this study, and did not use the values of activation energy or pre-exponential factor (for the pyrolysis model) developed in this work. Due to these factors, the temperatures at which the various area density states are reached could conceivably be different. Accordingly, the integrations were carried out for additional temperatures to facilitate a more precise implementation of this data by future numerical modelers.

176 Area εat 0 εat 15 εat 30 εat 45 εat 60 Temp (K) Density degree degree degree degree degree (mg/cm2 ) incidence incidence incidence incidence incidence 300 1.85 0.699 0.709 0.725 0.744 0.788 325 1.85 0.692 0.702 0.717 0.736 0.780 350 1.85 0.684 0.694 0.708 0.727 0.771 375 1.85 0.675 0.685 0.699 0.717 0.761 400 1.85 0.665 0.675 0.689 0.707 0.750 425 1.85 0.655 0.666 0.679 0.697 0.740 450 1.85 0.645 0.657 0.670 0.687 0.730 475 1.85 0.636 0.648 0.660 0.678 0.720 500 1.85 0.628 0.639 0.652 0.669 0.711 525 1.85 0.620 0.632 0.644 0.661 0.703 550 1.85 0.613 0.625 0.637 0.653 0.696 575 1.85 0.606 0.619 0.630 0.647 0.689 600 1.85 0.600 0.613 0.625 0.641 0.683 525 1.62 0.591 0.613 0.650 0.664 0.730 550 1.62 0.584 0.606 0.643 0.657 0.723 575 1.62 0.578 0.600 0.638 0.651 0.716 600 1.62 0.572 0.595 0.633 0.646 0.710 625 1.62 0.567 0.590 0.628 0.641 0.705 650 1.62 0.562 0.586 0.624 0.636 0.700 550 1.25 0.564 0.583 0.609 0.627 0.667 575 1.25 0.558 0.578 0.603 0.621 0.661 600 1.25 0.553 0.573 0.598 0.615 0.654 625 1.25 0.549 0.570 0.594 0.611 0.650 650 1.25 0.544 0.565 0.589 0.605 0.643 675 1.25 0.540 0.561 0.585 0.601 0.638 575 0.77 0.456 0.472 0.499 0.522 0.633 600 0.77 0.453 0.468 0.495 0.518 0.627 625 0.77 0.449 0.465 0.491 0.514 0.621 650 0.77 0.446 0.462 0.488 0.511 0.617 675 0.77 0.442 0.459 0.485 0.507 0.612 700 0.77 0.440 0.456 0.482 0.504 0.607 600 0.40 0.386 0.366 0.406 0.450 0.532 625 0.40 0.383 0.363 0.404 0.447 0.528 650 0.40 0.381 0.361 0.401 0.444 0.524 675 0.40 0.379 0.359 0.399 0.441 0.520 700 0.40 0.376 0.356 0.397 0.438 0.516 725 0.40 0.374 0.354 0.395 0.435 0.512 750 0.40 0.372 0.352 0.393 0.432 0.509 Table 19: Broad-band emittance values for all tested angles, at a range of Planck temperatures for each discrete area density.

177 11.0 Appendix VI: Contact Information to Obtain Complete Spectral Data Set

A complete set of data from both the final data set and the comparison cases discussed in

Section 4 is available electronically from the following sources:

Richard Pettegrew (author)

National Center for Space Exploration Research [email protected]

216-433-8321

Professor James T’ien

Case Western Reserve University [email protected]

216-368-4581

Dr. Kenneth Street

NASA Glenn Research Center [email protected]

216-433-5032

178 12.0 References

1. Ross. H., (editor), Microgravity Combustion: Fire in Free Fall, Academic Press (2001). 2. Bonne, U., Radiative Extinction of Diffusion Flames at Zero Gravity, Combustion and Flame, Vol. 16, pp. 147-159 (1971). 3. T’ien, J. S., Diffusion Flame Extinction at Small Stretch Rates: The Mechanism of Radiative Loss, Combustion and Flame, Vol. 65 pp. 31-34 (1986). 4. T’ien, J.S., The Role of Radiation on Microgravity Flames, Spacebound 2000 Conference, Vancouver, Canada (2000). 5. Jiang, C. B., A Model of Flame Spread over a Thin Solid in Concurrent Flow with Flame Radiation, Ph.D. Thesis, Case Western Reserve University, Cleveland, OH (1995). 6. Incropera, F.P., DeWitt, D.P., Fundamentals of Heat and Mass Transfer, 3rd Edition, Wiley & Sons (1990). 7. Siegel, R. and Howell, J.R., Thermal Radiation Heat Transfer, 3rd edition, Hemisphere Publishing Corp. (1992). 8. Ronney, P., Understanding Combustion Processes Through Microgravity Research, 27th Symposium on Combustion, Proceedings of the Combustion Institute, pp. 2485-2506 (1998). 9. Bhattacharjee, S., and Altenkirch, R.A., Radiation-Controlled, Opposed-Flow Flame Spread in a Microgravity Environment, , 23rd Symposium on Combustion, Proceedings of the Combustion Institute, pp. 1627-1633 (1990). 10. Rhatigan, J.L., Bedir, H., and T’ien, J.S., Gas-Phase Radiative Effects on the Burning and Extinction of a Solid Fuel, Combustion and Flame, Vol. 112, pp. 231-241 (1998). 11. Bedir, H., and T’ien, J.S., A Computational Study of Flame Radiation in PMMA Diffusion Flames Including Fuel Vapor Participation, 27th Symposium on Combustion, Proceedings of the Combustion Institute, pp. 2821-2828 (1998). 12. Moran, M.J., and Shapiro, H.N., Fundamentals of Engineering Thermodynamics, 2nd Edition, Wiley & Sons (1992). 13. McCluney, R., Introduction to Radiometry and Photometry, Artech House, Inc. (1994). 14. De Ris, J. N., Spread of a Laminar Diffusion Flame, 12th Symposium on Combustion, Proceedings of the Combustion Institute, pp. 241-252 (1969). 15. Bedir, H., T’ien, J. S. and Lee, H. S., Combustion Theory Modeling 1:395-404 (1997). 16. Daguse, T., Croonenbroek, T., Rolon, J.C., Darabiha,N., and Soufiani, A., Study of Radiative Effects on Laminar Counterflow H2/O2/N2 Diffusion Flames, Combustion and Flame, Vol. 106, pp. 271-287 (1996). 17. Ju, Y., Masuya, G., Ronney, P.D., Effects of Radiative Emission and Absorption on the Propagation and Extinction of Premixed Gas Flames, 27th Symposium on Combustion, Proceedings of the Combustion Institute, pp. 2619-2626 (1998). 18. Davies, M. (editor), Infrared Spectroscopy and Molecular Structure, Elsevier Publishing (1963).

179 19. Staaf, O., Ribbing, C.G., Andersson, S.K., Temperature Dependence of the Band Emittance for Nongray Bodies, Applied Optics, Vol. 35, No. 31, pp. 6120-6125. 20. Pettegrew, R.D., Street, K., Piltch, N.D., T’ien, J.S., Morrison, P., Measurement and Evaluation of the Radiative Properties of a Thin Solid Fuel, 41st AIAA Aerospace Sciences Conference, AIAA-2003-0511 (2003). 21. Kumar, A., Tolejko, K., T’ien, J.S., A Computational Study of Flame Radiation- Surface Interaction in Flame Spread Over a Thin Solid Fuel, Journal of Heat Transfer, Vol. 126, pp.611-620 (2004). 22. Rhatigan, J.L., Effect of Gas-Phase Radiation and Detailed Kinetics on the Burning and Extinction of a Solid Fuel, PhD. Thesis, Case Western Reserve University (2001). 23. Feier, I.I., graduate student, Case Western Reserve University, personal communication (2005). 24. Tolejko, K., graduate student, Case Western Reserve University, personal communication (2004). 25. Kleinhenz, J.E., Feier, I.I., Pettegrew, R.D., Sacksteder, K.R., Ferkul, P.V., T’ien, J.S., Infrared Imaging Diagnostics for Flame Spread Over Solid Surfaces, 41st AIAA Aerospace Sciences Conference, AIAA-2003-988 (2003). 26. Arakawa, A., Saito, K., Gruver, W.A., Automated Infrared Imaging Temperature Measurement with Application to Upward Flame Spread Studies, Part I, Combustion and Flame, Vol. 92, pp. 222-230 (1993). 27. Haugh, M.J., Infrared Thermometry for Low Emissivity Metals, ISA Transactions, Vol. 22, No. 3, pp. 27-31 (1983). 28. Olstad, S.J., Tanaka, F., DeWitt, D.P., Evaluation of a Method for Measuring Spectral Emissivity at Moderate Temperatures, 20th AIAA Thermophysics Conference, AIAA TP-85-0091 (1985). 29. Zhang, Y.W., Zhang, C.G., Klemas, K., Quantitative Measurements of Ambient Radiation, Emissivity, and Truth Temperature of a Greybody: Methods and Experimental Results, Applied Optics, Vo. 25, No. 20, pp. 3683-3689. 30. Pettegrew, R.D., Piltch, N.P., Ferkul, P.V., Emissivity Measurement of a Thin, Pyrolyzing Fuel, 37th AIAA Aerospace Sciences Conference, AIAA 99-0700 (1999). 31. Piltch, N.P., Pettegrew, R.D., Ferkul, P.V., Quantitative Surface Emissivity and Temperature Measurements of a Burning Solid Fuel Accompanied by Soot Formation, 39th AIAA Aerospace Sciences Conference, AIAA 2001-0627 (2001). 32. Hanssen, L., Integrating-Sphere System and Method for Absolute Measurement of Transmittance, Reflectance, and Absorptance of Specular Samples, Applied Optics, Vol. 40, No. 19, pp. 3196-3204 (2001). 33. Serio, M.A., Pines, D.S., Bonanno, A.S., Solomon, P.R., Simons, G.A., An Instrument for Characterization of the Thermal and Optical Properties of Charring Polymeric Materials, 25th Symposium on Combustion, Proceedings of the Combustion Institute, pp. 1447-1453 (1994). 34. Morrson, P., Pettegrew, R.D., Street, K., Piltch, N.P., T’ien, J.S., Spectrally Resolved Radiative Properties of Thin Cellulosic Fuels, 40th AIAA Aerospace Sciences Conference, AIAA 2002-0919 (2002).

180 35. Ferkul., P.V., Kleinhenz, J.E., Shih, H.Y., Pettegrew, R.D., Sacksteder, K.R., T’ien, J.S., Solid Fuel Combustion Experiments in Microgravity Using a Continuous Fuel Dispenser and Related Numerical Simulations, Microgravity Science and Technology (May 2004). 36. Grayson, G.D., Sacksteder, K.R., Ferkul, P.V., T’ien, J.S., Flame Spreading Over a Thin Fuel in Low Speed Concurrent Flow: Droptower Experimental Results and Comparison with Theory, Microgravity Science and Technology VII/2, pp.187- 195 (1994). 37. Feier, I.I., Shih, H.Y., Sacksteder, K.R., T’ien, J.S., Upward Flame Spread Over Thin Solids in Partial Gravity, Proceedings of the Combustion Institute, Volume 29, pp. 2569-2577 (2002). 38. Olson, S.L., Kashawagi, T., Fujita, O., Kikuchi, M., Ito, K., Experimental Observations of Spot Radiative Ignition and Subsequent Three-Dimensional Flame Spread over Thin Cellulose Fuels, Combustion and Flame, Vol. 125, pp. 852-864 (2001). 39. Personal communication, Technical Support at Thermo-Nicolet Instrument Company, phone number 800-532-4752 (2005). 40. Bartkus, T.P., Ignition and Combustion of Single Black Liquor Droplets in Normal Gravity and Reduced Gravity, Masters Thesis, Case Western Reserve University, Cleveland, OH (2004). 41. Bhattacharjee, S., Altenkirch, R.A., Olson, S.L., Sotos, R.G., Heat Transfer to a Thin Solid Combustible in Flame Spreading at Microgravity, Journal of Heat Transfer, Vol. 113, pp. 670-676 (1991). 42. O’Connor, R.T., Analysis of Chemically Modified Cotton, in Cellulose and Cellulose Derivatives, Volume 4, Bikales N.M., and Segal, L. (eds), Wiley & Sons, NY (1971). 43. Dyer, J.R., Applications of Absorption Spectroscopy of Organic Compounds, Prentice-Hall (1965). 44. Hamilton, D.C., and Morgan, W.R., Radiant Interchange Configuration Factors, National Advisory Committee for Aeronautics, Technical Note 2836, 1952. 45. Skoog, D.A., West, D.M., Principles of Instrumental Analysis, 2nd Edition, Saunders College/Holt, Rinehart and Winston (1980). 46. Ferraro, J.R., Basile, L.J., Fourier Transform Infrared Spectroscopy: Applications to Chemical Systems, Volume 1, Academic Press (1978). 47. Griffiths, P.R., de Haseth, J.A., Fourier Transform Infrared Spectrometry, Wiley- Interscience/Wiley & Sons (1986). 48. Mendenhall, W., Sincich, T., Statistics for Engineering and the Sciences, 3rd Edition, Dellen/Macmillan Publishing (1992). 49. Pettegrew, R.D., An Experimental Study of Ignition Effects and Flame Growth Over a Thin Solid Fuel in Low-Speed Concurrent Flow Using Drop-Tower Facilities, Masters Thesis, Case Western Reserve University, Cleveland, OH (1995) and NASA CR-198537 (1996). 50. Ferkul, P.V., A Model of Concurrent Flow Flame Spread Over a Thin Solid Fuel, NASA CR-191111 (1993).

181