Development, verification, and validation of the responsive boundary model for pool fire simulations

The need to understand and predict the behavior of fires and explosions is important considering the amount of property damage and the loss of life that can result. In the case of transportation pool fires (fires resulting from liquid fuel spills), predictive science is an especially valuable tool considering that experiments with large pools fires are costly and often lead to damaged or destroyed instrumentation. In the development of fire codes as well as in other areas of computational science, the need for fidelity in computational results has become a prominent issue. The various sources of error in computation, such as discretization error, machine round-off error, iterative convergence error, programmer error, and model error, must be accounted for and, if possible, quantified if computational results are to be considered legitimate. The current study seeks to remedy an important source of error in pool fire simulations. The error stems from the application of a simplistic fuel inlet boundary condition. Traditionally this type of boundary condition assumes that the liquid pool vaporizes fuel to feed the flame at a constant rate. Additionally the vaporization rate is assumed to be uniform over the pool surface. In reality there is a complex feedback mechanism between the pool surface and the flame. Pool vaporization rate changes with time as the pool is heated, and thermal flux to the pool will be nonuniform over the surface. The responsive Boundary model utilizes energy and mass conservation principles to model the thermal behavior of the fuel pool and to predict the vaporization rate given thermal input from the flame. Verification tests such as the Method of Manufactured Solutions and grid convergence and validation methods such as model input sensitivity analysis and consistency analysis are applied to the Responsive Boundary model on its own and linked with the gas-phase fire code (ARCHES). The tests verify that the code solves the continuum model that is the basis of the boundary model with acceptable error. A region of consistency is also found between the steady vaporization fluxes predicted from the model and experimental data for a small heptane pool fire. Consistency analysis is also applied to data obtained from ARCHES simulations of a small helium plume and data taken from holographic interferometric images.

DEVELOPMENT, VERIFICATION, AND VALIDATION OF THE RESPONSIVE BOUNDARY MODEL FOR POOL FIRE SIMULATIONS by Weston M. Eldredge A dissertation submitted to the faculty of The University of Utah in partial fulfillment of the requirements for the degree of Doctor of Philosophy Department of Chemical Engineering The University of Utah August 2011 Copyright c Weston M. Eldredge 2011 All Rights Reserved T h e U n i v e r s i t y o f U t a h G r a d u a t e S c h o o l STATEMENT OF DISSERTATION APPROVAL The dissertation of Weston M. Eldredge has been approved by the following supervisory committe members: Philip J. Smith , Chair May 25, 2011 Date Approved Milind D. Deo , Member May 4, 2011 Date Approved Eric G. Eddings , Member May 4, 2011 Date Approved Aaron Fogelson , Member May 4, 2011 Date Approved Edward M. Trujillo , Member May 4, 2011 Date Approved and by JoAnn S. Lighty , Chair of the Department of Chemical Engineering and by Charles A. Wight, Dean of The Graduate School. ABSTRACT The need to understand and predict the behavior of fires and explosions is important considering the amount of property damage and the loss of life that can result. In the case of transportation pool fires (fires resulting from liquid fuel spills), predictive science is an especially valuable tool considering that experiments with large pools fires are costly and often lead to damaged or destroyed instrumentation. In the development of fire codes as well as in other areas of computational science, the need for fidelity in computational results has become a prominent issue. The various sources of error in computation, such as discretization error, machine round-off error, iterative convergence error, programmer error, and model error, must be accounted for and, if possible, quantified if computational results are to be considered legitimate. The current study seeks to remedy an important source of error in pool fire simulations. The error stems from the application of a simplistic fuel inlet boundary condition. Tradi-tionally this type of boundary condition assumes that the liquid pool vaporizes fuel to feed the flame at a constant rate. Additionally the vaporization rate is assumed to be uniform over the pool surface. In reality there is a complex feedback mechanism between the pool surface and the flame. Pool vaporization rate changes with time as the pool is heated, and thermal flux to the pool will be nonuniform over the surface. The Responsive Boundary model utilizes energy and mass conservation principles to model the thermal behavior of the fuel pool and to predict the vaporization rate given thermal input from the flame. Verification tests such as the Method of Manufactured Solutions and grid convergence and validation methods such as model input sensitivity analysis and consistency analysis are applied to the Responsive Boundary model on its own and linked with the gas-phase fire code (ARCHES). The tests verify that the code solves the continuum model that is the basis of the boundary model with acceptable error. A region of consistency is also found between the steady vaporization fluxes predicted from the model and experimental data for a small heptane pool fire. Consistency analysis is also applied to data obtained from ARCHES simulations of a small helium plume and data taken from holographic interferometric images. iv CONTENTS ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii LIST OF FIGURES. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xii ABBREVIATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii NOTATION AND SYMBOLS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiv ACKNOWLEDGEMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxii CHAPTERS 1. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Background and Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Development of CFD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 Pool Fires . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.4 Research Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.4.1 Objective 1: Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.4.2 Objective 2: Verification and Validation . . . . . . . . . . . . . . . . . . . . . . . . 11 2. THEORETICAL BACKGROUND . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.2 Review of Pool Fire Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.3 Important Pool Fire Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 2.4 The Pool Energy Balance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2.5 General Properties of Pool Flames . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 2.6 General Properties of the Liquid Pool . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 2.7 Properties of Pool Fire Radiation and Convection . . . . . . . . . . . . . . . . . . . . . 39 2.8 Previous Liquid Pool Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 2.8.1 Model 1: Prasad et al. (1999) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 2.8.2 Model 2: Novozhilov and Koseki (2004) . . . . . . . . . . . . . . . . . . . . . . . . 47 2.8.3 Model 3: Brown and Vembe (2006) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 2.9 Methods of Model Verification, Validation, and Error Quantification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 2.9.1 Methods of Verification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 2.9.2 A Method of Validation: Data Collaboration . . . . . . . . . . . . . . . . . . . . 56 3. RESPONSIVE BOUNDARY MODEL DESCRIPTION . . . . . . . . . . . . 71 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 3.2 Physical Domain and Conversation Equations . . . . . . . . . . . . . . . . . . . . . . . . 72 3.2.1 The Energy Balance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 3.2.2 Mass and Species Balances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 3.2.3 Discretization Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 3.3 Mass Burn Rate Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 3.4 Physical Property Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 3.5 Liquid Drop and Interpolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 3.6 Overview of the Responsive Boundary Code . . . . . . . . . . . . . . . . . . . . . . . . . 88 3.7 Interaction with ARCHES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 4. VERIFYING AND VALIDATING THE RESPONSIVE BOUNDARY MODEL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 4.2 Verification: Manufactured Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 4.2.1 Grid Convergence Tests with the Manufactured Solutions . . . . . . . . . . 100 4.3 Verification: Grid Convergence of Model Output and Grid Convergence Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 4.4 Validation: Sensitivity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 4.5 Comparison with Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 5. DATA COLLABORATION: SMALL HELIUM PLUMES . . . . . . . . . . . 137 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 5.2 Holographic Interferometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 5.3 Important Mathematical Relations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 5.4 Helium Plume Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 5.5 Consistency Analysis: First Iteration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 5.5.1 Pairwise Consistency Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 5.5.2 Analysis of the Full Set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 5.6 Consistency Analysis: Final Iteration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 6. ARCHES WITH THE RESPONSIVE BOUNDARY . . . . . . . . . . . . . . . 170 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170 6.2 General Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171 6.3 Simulated Pool Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172 6.4 A Computational Issue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176 6.5 Grid Convergence Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177 6.6 Consistency Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181 7. CONCLUSIONS AND FUTURE WORK . . . . . . . . . . . . . . . . . . . . . . . . . 215 7.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215 7.2 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218 7.3 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222 vi LIST OF FIGURES 1.1 The validation hierarchy for the problem of determining heat flux to a con-tainer engulfed in a large transportation pool fire. . . . . . . . . . . . . . . . . . . . . . . 16 1.2 A smaller hierarchy where the efforts of the present research are focused. . . . . 17 2.1 A pool fire with the modes of heat transfer labeled. . . . . . . . . . . . . . . . . . . . . 61 2.2 The qualitative behavior of liquid pool regression rate versus pool diameter based on Hottel's (1958) analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 2.3 A sketch of basic pool fire flame shapes at different burning phases. . . . . . . . . 63 2.4 A qualitative sketch of temperature data common to most burning pools. . . . 64 2.5 The electro-magnetic spectrum with the thermal radiation portion labeled. . . 65 2.6 The dynamics of radiation interaction with the pool. . . . . . . . . . . . . . . . . . . . 66 2.7 The reflection and refraction of light passing between two transparent media. Relevant angles are also shown. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 2.8 The surface reflectivities of incident radiation as a function of incident angle for media of different refractive indexes (RI). Incident angle is defined in Figure 2.7. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 2.9 The process of computational model development adapted from a chart pro-vided by Oberkampf and Trucano (2002). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 2.10 A contrived example of data/model comparison. . . . . . . . . . . . . . . . . . . . . . . . 70 3.1 The computational domain of the liquid pool for the Responsive Boundary model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 3.2 Fluid/fluid mass transfer according to film theory. . . . . . . . . . . . . . . . . . . . . . 92 3.3 How the computational domain changes with liquid drop. . . . . . . . . . . . . . . . . 93 3.4 The top nodes of the pool domain and the location of the extrapolated surface temperature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 3.5 A depiction of the three-dimensional domain of a pool fire in ARCHES. . . . . . 95 4.1 The output from the Responsive Boundary model for a manufactured solution to the energy balance equation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 4.2 The relative error in the output from the Responsive Boundary model for a manufactured solution of the energy equation. . . . . . . . . . . . . . . . . . . . . . . . . . 115 4.3 The model output for the manufactured solution for the height equation. . . . . 116 4.4 A log plot of the error in the model output for the manufactured solution for the height equation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 4.5 A log plot that confirms the order of error for the energy equation with respect to spatial step size. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 4.6 A log plot that confirms the order of error for the energy equation with respect to time step size. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 4.7 A log plot that confirms the order of error in the height equation with respect to time step size. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 4.8 The response of the model output to radiative heat flux. . . . . . . . . . . . . . . . . . 121 4.9 The response of the model output to flame temperature. . . . . . . . . . . . . . . . . . 122 4.10 The response of the model output to variation in wind speed. . . . . . . . . . . . . . 123 4.11 The response of the model output to variation in system pressure. . . . . . . . . . 124 4.12 The response of the model output to variation in system temperature. . . . . . . 125 4.13 The response of the model output to variation in pool surface reflectivity. . . . 126 4.14 The simulated burn rate based on experimental conditions from case one from Blanchat et al. (2006). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 4.15 The simulated burn rate based on experimental conditions for case two from Blanchat et al. (2006). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 4.16 The simulated burn rate based on experimental conditions for case three from Blanchat et al. (2006). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 4.17 The simulated burn rate based on experimental conditions for case four from Blanchat et al. (2006). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 4.18 The simulated burn rate based on experimental conditions for the 30-centimeter heptane case from Klassen and Gore (1992). . . . . . . . . . . . . . . . . . . . . . . . . . . 131 4.19 The simulated burn rate based on experimental conditions for the 30-centimeter methanol case from Klassen and Gore (1992). . . . . . . . . . . . . . . . . . . . . . . . . . 132 4.20 The flame temperature for a 30-centimeter heptane pool fire simulated in ARCHES. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 4.21 The heptane mass fraction above the pool for a 30-centimeter heptane pool fire simulated in ARCHES. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 5.1 An example of an original interferogram of a helium plume. . . . . . . . . . . . . . . 152 5.2 How holographic images of helium plumes are produced. . . . . . . . . . . . . . . . . . 153 5.3 Interference order data from an ARCHES simulation of a helium plume. . . . . 154 5.4 A density contour plot from a helium simulation in ARCHES. . . . . . . . . . . . . 155 5.5 The data comparison of the interference order between experiment (in black) and computation (in red) at different radial positions at a height of 3 cen-timeters above the helium inlet. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156 viii 5.6 The data comparison of the interference order between experiment (in blue) and computation (in red) at different radial positions at a height of 5 cen-timeters above the helium inlet. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 5.7 A comparison of simulation output from the base-case simulation run at three different resolutions for the data at 3 centimeters above the helium inlet. . . . . 158 5.8 A comparison of simulation output from the base-case simulation run at three different resolutions for the data at 5 centimeters above the helium inlet. . . . . 159 5.9 Consistency measures for all pair-wise analyses involving dataset units 1 through 11. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160 5.10 Consistency measures for all pair-wise analyses involving dataset units 12 through 22. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161 5.11 The values of the Lagrangian multipliers for the original helium dataset. The consistency measure for this set is -2.96, indicating an inconsistent set. . . . . . 162 5.12 The values of the Lagrangian multipliers for the reduced dataset where one point (12) has been removed. The consistency measure for this set is -2.47, indicating an inconsistent set. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 5.13 The values of the Lagrangian multipliers for the reduced dataset where two points (12 and 13) have been removed. The consistency measure for this set is -1.51, indicating an inconsistent set. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164 5.14 This bar graph shows the values of the Lagrangian multipliers for the re-duced dataset where three points (12, 13, and 1) have been removed. The consistency measure for this set is -0.72, indicating an inconsistent set. . . . . . 165 5.15 The values of the Lagrangian multipliers for the reduced dataset where four points (12, 13, 1, and 22) have been removed. The consistency measure for this set is 0.51, indicating a consistent set. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166 5.16 The same data as that seen in Figure 5.5 with the error bars revised. . . . . . . . 167 5.17 The same data as that seen in Figure 5.6 with the error bars revised. . . . . . . . 168 6.1 The mass flux from the pool surface at a simulation time of 0.5 seconds. This time is during the transient warm up phase of the pool fire. . . . . . . . . . . . . . . 189 6.2 The same type of data as that shown in Figure 6.1 at a simulation time of 7.0 seconds. This time is considered to be during the steady burn phase of the pool fire. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190 6.3 The mass fraction of heptane (the fuel) in the gas phase just over (about 2.25 millimeters) the pool surface during the transient burning phase. . . . . . . . . . . 191 6.4 The mass fraction of heptane (the fuel) in the gas phase just over (2.25 millimeters) the pool surface during the steady burning phase. . . . . . . . . . . . . 192 6.5 The liquid surface temperature of the pool during the transient burning stage.193 6.6 The liquid surface temperature of the pool during the steady burning stage. . 194 ix 6.7 The incident radiative heat flux to the pool surface for the transient phase of the pool fire. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195 6.8 The incident radiative heat flux to the pool surface for the steady phase of the pool fire. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196 6.9 The convective heat flux to the pool surface at the transient phase of the pool fire. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197 6.10 The convective heat flux to the pool surface at the steady phase of the pool fire. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198 6.11 A two-dimensional side view of the pool fire. The data are the gas phase temperature profiles of the pool fire during the transient stage. . . . . . . . . . . . . 199 6.12 A two-dimensional side view of the pool fire. The data are the gas phase temperature profiles of the pool fire during the steady stage. . . . . . . . . . . . . . 200 6.13 A plot of global mass flux from the pool surface with time. As of 30 seconds of simulation time steady state is not yet obtained. . . . . . . . . . . . . . . . . . . . . . 201 6.14 The spatially averaged radiative heat flux to the pool surface against simu-lation time. These data arise from the same simulation used for the data in Figure 6.13. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202 6.15 The global mass flux for another heptane simulation like the one shown in Figure 6.13. However, this simulation accelerates the pool's response by a factor of 10 for the first 3 seconds of simulation time. . . . . . . . . . . . . . . . . . . . 203 6.16 The global mass burn flux from the pool surface for several heptane pool simulations at different spatial resolutions. . . . . . . . . . . . . . . . . . . . . . . . . . . . 204 6.17 The global radiative heat flux to the pool surface for several heptane pool simulations at different spatial resolutions. . . . . . . . . . . . . . . . . . . . . . . . . . . . 205 6.18 The global convective heat flux to the pool surface for several heptane pool simulations at different spatial resolutions. . . . . . . . . . . . . . . . . . . . . . . . . . . . 206 6.19 The global mass burn flux from the pool surface for several methanol pool simulations at different spatial resolutions. . . . . . . . . . . . . . . . . . . . . . . . . . . . 207 6.20 The global radiative heat flux to the pool surface for several methanol pool simulations at different spatial resolutions. . . . . . . . . . . . . . . . . . . . . . . . . . . . 208 6.21 The global convective heat flux to the pool surface for several methanol pool simulations at different spatial resolutions. . . . . . . . . . . . . . . . . . . . . . . . . . . . 209 6.22 The simulation and experimental data with their ranges for the global, steady mass burn flux. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210 6.23 The simulation and experimental data with their ranges for the different radiative heat fluxes. Note that a pool radius of zero centimeters denotes the center of the pool. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211 6.24 Consistency measures for all the pair-wise consistency tests associated with the heptane pool fire dataset. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212 x 6.25 The values of each Lagrangian multiplier for each component of the full consistency analysis for the heptane pool fire system. . . . . . . . . . . . . . . . . . . . 213 xi LIST OF TABLES 4.1 The data for the grid convergence of liquid temperature with spatial step. . . 135 4.2 The data for the grid convergence of mass burn rate with spatial step size. . . 135 4.3 The data for the grid convergence for mass burn rate with time step size. . . . 135 4.4 The grid convergence data for the liquid height with time step size. . . . . . . . . 135 4.5 Data for the grid convergence of mass burn rate without interpolation. . . . . . 136 4.6 Test conditions and results for the simple sensitivity analysis. . . . . . . . . . . . . 136 4.7 Simulation input data taken from experimental pool fires. . . . . . . . . . . . . . . . 136 4.8 A comparison of simulation and experimental results. . . . . . . . . . . . . . . . . . . 136 5.1 The proposed active variables and their relevant information for the helium plume simulations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169 5.2 The values for the inputs used in each simulation for the Box-Behnken designed helium plume simulations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169 6.1 Data from all five simulations for the consistency analysis. The results for the steady, global mass flux (kg/m2 − sec) and the average incident radiation flux (W/m2) at the pool center, and at pool radii of 2, 4, 6, 8, 10, 12, 13, and 14 centimeters are shown. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214 6.2 Consistency results for tests on the whole 10-member dataset. Each test assumes different levels of experimental error. The percentages along the top of the table represent mass burn rate error, and those along the left side of the table represent radiative heat flux error. . . . . . . . . . . . . . . . . . . . . . . . . . 214 ABBREVIATIONS CFD Computational Fluid Dynamics C-SAFE Center for the Simulation of Accidental Fires and Explo-sions DNS Direct Numerical Simulation GCI Grid Convergence Index HFG Heat Flux Gauge LES Large Eddy Simulation MMS Method of Manufactured Solutions RANS Reynolds-Averaged Navier Stokes RI Refractive Index NOTATION AND SYMBOLS A Area bii Generic quadratic model fit parameters (Equation 5.3) Cf Fluid heat capacity (Equation 2.13) Ci Concentration of species i in pool liquid Cp Heat capacity (Equation 3.1 - 3.3) Cp, g Gas phase heat capacity Ct Total concentration in gas/liquid interphase film C" Consistency measure d Pool diameter (Equation 2.3) Da, b Bindary diffusivity of species a and b F Geometric view factor g, gi Gravitational acceleration in the ith direction h Heat transfer coefficient hm Mass transfer coefficient Hc Heat of combustion Hevap Heat of vaporization Hv Heat of vaporization Hvap Heat of vaporization E Energy fn + 1( ) The n+1 derivative of function f evaluated at , used to determine Lagrangian interpolation error (Equation 3.21) fexact Exact solution for a continuum equation fi Solution to a continuum model solved on grid i fmax Maximum sensible heat fraction parameter (Equation 2.21) fsensible Fraction of thermal input used to heat the pool Fs Error enhancement parameter for the GCI (Equation 2.33) [GCI] Grid convergence index (Equation 2.33) Gr Grashof number Gr! Diffusional Grashof number h Heat transfer coefficent from Newton's law of cooling (Equation 2.12) hm Mass transfer coefficient (Equation 2.18) h Pool liquid height (Equations 2.22 and 2.23) H Pool liquid height (Equation 3.4) Hevap Heat of vaporization Hfg Heat of vaporization H Hypercube that represents a model input parameter space I(z) Intensity of electro-magnetic wave as a function of pool depth z I0 Incident intensity of electro-magnetic wave as it passes the pool surface k Parameter that characterizes temperature profile in the liquid pool (Equation 2.5) k Generic constant used in defining Taylor series error terms (Equation 2.26) k Thermal conductivity (Equation 3.1) k1, k2 Parameters used to fit pool temperature profile (Equation 3.22) k1, k2, k3, k4 Intermediate parameters for Runga-Kutta method (Equa-tions 3.6 and 3.7) kc Mass transfer coefficient (Equation 3.10) kf Fluid thermal conductivity (Equation 2.16) xv [ki] Mass transfer coefficient matrix evaluated at location i kl Thermal conductivity l Characteristic length associated with the Reynolds number (Equation 2.2) le Lower bound of experimental data uncertainty L Characteristic length associated with the definitions of the Grashof numbers (Equations 3.11 and 3.12) and the mass transfer coefficient (Equation 3.16) Le Lewis number m Mass of liquid in pool (Equation 2.24) m˙ Mass vaporization rate of fuel m00 Mass flux from the pool surface due to evaporation m00evap Mass flux from the pool surface due to evaporation (Equa-tion 3.4) n Correlation parameter (Equation 2.19) n0 Standard refractive index (usually for pure air) for use in the optical path length difference relation (Equation 5.1) ni Refractive index of medium i nm(x, y, z, t) Refractive index as a function of both space and time, used in the optical path length difference relation (Equation 5.1) N Vector of molar fluxes in a multi-component system N0, i Specific refractivity of species i N00evap Molar flux of fuel from pool surface due to evaporation p, P Fluid pressure p Order of grid convergence error (used in Equations 2.30 and 2.31) pk(x) The kth Lagrangian polynomial evaluated at spatial coor-dinate x P1 Reference pressure in Clausius-Clapeyron equation (Equa-tion 2.15) xvi Pcc Clausius-Clapeyron vapor pressure Pn(x) An interpolated function value as a function of spatial coordinate x, based on a series of Lagrangian polynomials Ps, i Saturation pressure of species i for use in VLE model (Equation 3.18) Pvap Partial pressure of fuel in vapor phase q Generic term for heat transfered q00 Generic term for heat flux q00conv Heat flux due to convection q00convection Heat flux due to convection q00evap Energy flux due to evaporation of fuel from the pool (Equa-tion 3.3) q00incident Incident radiative heat flux to pool surface qmms Source term used with manufactured solutions q00re − rad Heat flux radiating from the pool surface q00total, pool Net input of heat to the pool (Equations 2.20 - 2.24) q Source term for the scalar balance (Equation 1.3) Qabs Thermal input to the pool surface (Equation 2.13) Qc Heat release due to fuel combustion Qf Thermal input to pool surface (Equation 2.13) r Grid refinement ratio (used in Equations 2.30 and 2.31) rb Liquid regression rate (Equation 2.13) R Pool surface reflectivity, also universal gas constant Rn(x) Error associated with use of Lagrangian polynomial inter-polation as a function of spatial coordinate x Rp Surface reflectivity for light polarized parallel to the inter-face plane of interest xvii Rs Surface reflectivity for light polarized perpendicular to the interface plane of interest Re Reynolds number S(x, y, t) Interference order as a function of spatial coordinates x and y and of time t Sh Overall Sherwood number Shforced Sherwood number associated with forced convection Shfree Sherwood number associated with buoyancy driven convec-tion t Time or temporal coordinate tend Time at wihich manufactured solution for the mass balance drops to a value of zero t Temporal step size T, T(z) Liquid temperature as a function of liquid depth T0, T1 Ambient temperature T1 Reference temperature in Clausius-Clapeyron relation (Equation 2.15) Tb Parameter for pool energy balance model (Equation 2.21) Tb Boiling point temperature TB Pool temperature (Equation 2.3) Tcc Temperature at which Clausius-Clapeyron vapor pressure is computed (Equation 2.15) Tf Flame Temperature Tnominal Nominal temperature parameter used in the manufactured solution to the energy balance equation (Equation 4.1) Ts Pool surface temperature Tpool Pool liquid temperature (Equations 2.21 and 2.22) ue Upper bound of experimental data uncertainty ui Fluid velocity in the ith direction xviii u1 Bulk flow fluid velocity U Heat transfer coefficient (Equation 2.3) U Generic quantity of interest (Equation 2.25) v Liquid regression rate (Equation 2.4) v1 Maximum liquid regression rate parameter (Equation 2.4) V Volume x Vector of input parameters to a model x, xi Spatial coordinate in the ith direction x0 Mole fraction vector, liquid phase side of film xbulk Fuel mole fraction in the bulk gas phase (Equation 3.10) xi Fuel mole fraction at gas/liquid film (Equation 3.10) xi Liquid phase mole fraction of species i for use in VLE model (Equation 3.18) x Mole fraction vector, gas phase side of film Xvap Mole fraction of fuel in vapor phase y Spatial coordinate y(x1, x2, x3) Function output for quadratic model as a function of model inputs x1, x2, and x3 (Equation 5.3) yi Gas phase mole fraction of species i for use in VLE model (Equation 3.18) ye Experimental measure of some quantity Ye Ye Physical quantity of interest to be measured or predicted ym(x) model prediction as a function of model inputs x YF,1 Mass fraction of fuel in the bulk gas phase YF, s Mass fraction of fuel at gas/liquid interface z Spatial coordinate often associated with pool depth, also used along the beam path in holographic interferometry z Spatial step size in pool domain xix absorption coefficient defined in Equation 2.8 Pool surface absorptivity (Equation 2.20) Thermal diffusivity (Equation 2.27 - 2.29) Parameter used with manufactured solution for the mass balance equation (Equation 4.2) j Lower bound of uncertainty in model input parameter j Thermal expansion coefficient associated with the Grashof number (Equation 3.11) [ i] Bootstrap matrix evaluated at location i j Upper bound uncertainty in model input parameter j Adjustment parameter for uncertainty bounds in experi-mental data, used to determine consistency (Equation 2.38) i Liquid phase activity coefficient of species i for use in VLE model (Equation 3.18) i Mass fraction of species i used with the Gladstone-Dale relation (Equation 5.2) 􀀀 Parameter that characterizes a diffusive velocity in the scalar balance (Equation 1.3) Thickness of gas/liquid film Symbol that denotes a change or perturbation in a quantity @ Parital differentiation symbol Emissivity Fractional error between continuum model solutions from two different grid resolutions (Equation 2.32) " Experimental data space i Angle of incident light Beer's law extinction coefficient Wavelength of electro-magnetic wave f Fluid thermal conductivity (Equation 2.13) xx (i) j Lagrangian multiplier for jth quantity of uncertainty type i Fluid kinematic viscosity Compositional expansion coefficient associated with the diffusional Grashof number (Equation 3.12) [ i] Bulk flow effect matrix evaluated at location i Mathematical constant , f Fluid density g Gas phase density Stefan-Boltzman constant ij Value of the stress tensor associated with directions i and j Conserved scalar quantity (Equation 1.3) Combustion efficiency !i Mass fraction at location i xxi ACKNOWLEDGEMENTS To Doctor Philip Smith for his seemingly unending supply of patience and his willing-ness to let me figure things out on my own. To my parents Fred and Jannis Eldredge who are largely the reason for what I am today. CHAPTER 1 INTRODUCTION 1.1 Background and Motivation Early in the morning on April 29, 2007 a gasoline tanker lost control and struck a pylon on a freeway interchange near the San Francisco-Oakland Bay Bridge. According to the Associated Press (2007), the tanker carried 8,600 gallons of gasoline that spilled and ignited. Observers of the accident noted that the resulting flames rose 200 feet in the air. The flames engulfed another highway interchange just above the accident scene. The heat from the flame melted the second interchange and caused a 250 foot section of the highway to collapse to the ground below. The accident destroyed a busy section of highway that serves nearly 100,000 vehicles each day. It required months to rebuild the destroyed section of highway, and in that time, the accident led to massive disruptions of city transportation. Although it was a costly accident, fortunately no lives were lost. Humankind has made use of fire for roughly 400,000 years. Fire has enabled them to cook food, allowing for an increased intake of nutrition. Fire use has provided a stable and relatively easily manipulated source of heat, allowing for the habitation of colder climates. In more modern times, the use of fire and other combustion reactions has benefited humankind in the generation of power, the advancement of industry, the use of improved systems of transportation, etc. However the use of fire gives rise to issues of safety, and not all fire scenarios are without the loss of life. According to the U.S. Fire Administration (2009), statistics for the year 2008 include the following facts: There were an estimated 1.5 million fires that year. 3,200 civilians and 118 firefighters lost their lives as a result of fire, and 16,705 civilians were injured. Direct property damage was estimated at 15.5 billion dollars. In 2008 fire claimed more human lives than all other natural disasters combined. Most of the lives and damages were results of residential fires. Nonresidential 2 fires (fires in public buildings, forest fires, and industrial fires) resulted in over 3.8 billion dollars (U.S. currency) in property damage. To save lives and cost, it is the objective of governmental, educational, and industrial researchers to develop materials and methods for the prevention of fires and the promotion of fire safety. For example, laws have been enacted that govern the layout of building plans to facilitate fire safety. Fire suppression systems have been developed and implemented to respond to fire in a variety of situations. Fire-resistant materials have been developed to protect firefighters in their work. Similar fire-resistant materials are also used in building and facility construction to prevent property damage. Large sums of revenue are invested by governmental agencies to educate the public on fire safety practices. Industrial and military organizations also invest a significant amount of time and money to protect lives and assets from fire damage. For some branches of research, the objective is to discover the physical laws and mech-anisms that govern fires and other combustion reactions in order to aid in the development of methods to promote fire safety and to utilize fire more efficiently for the benefit of society. Controlled fire experiments conducted by researchers seek to explore such issues as the reactions and reaction mechanisms involved in different combustion processes, the important modes of heat transfer involved in the resulting flames, the behavior of the flow fields produced in fires, the different chemical byproducts produced in fire reaction, and so forth. Because of the dangerous nature of fire, it is common for experimental equipment to suffer damage. For example, the measurements of radiative heat flux in a large fire often involve radiometers being engulfed in the flames. The cost of such experiments can be prohibitive, and the larger the fire the more costly the experiment. The resources of computational science, if sufficiently developed, can provide a more cost effective way of predicting and analyzing the behavior of fire systems. In the past, the complexity of combustion systems has made meaningful simulation of such systems nearly impossible. With the ongoing advancement of computing systems in terms of processing speed, memory storage capacity, and parallelization, these limitations have become more relaxed, and the capabilities of predictive science in fire systems have expanded. The growth of computational science does not eliminate the need for experiment. For computer models 3 to be of use, they must be developed using experimental data, and computational results must be validated against experiment. Once appropriately developed and proven however, computer models minimize the need for costly experimentation. 1.2 Development of CFD Modeling combustion systems requires the application of conservative relations for fluid systems. The conservation of mass, momentum, and energy is the foundational model for computational fluid dynamics (CFD). The resulting equations are called the Navier-Stokes equations. These equations can be expressed in differential or integral form. The differential form of the mass and momentum conservation equations are: @ @t + @ 􀀀 ui @xi = 0, (1.1) and @ 􀀀 ui @t + @ uiuj @xj = @ ij @xj − @p @xi + gi. (1.2) Here, is the fluid density, ui is the fluid velocity in the ith direction, t is the temporal coor-dinate, xi is the spatial coordinate in the ith direction, gi is the component of gravitational acceleration in the ith direction, p is the fluid pressure, and ij is the viscous stress tensor. These two equations are sufficient to describe isothermal, fluid systems with no chemical reactions. Combustion systems, however, are not isothermal and involve thousands of reactions. To describe such systems it is necessary to include scalar balances with the mass and momentum balances. For a combustion system, scalars of interest include, but are not necessarily limited to, energy and species concentration. The differential form of the scalar conservation equation is: @ ( ) @t + @ uj @xj = @ @xj 􀀀 @ @xj ! + q . (1.3) 4 In this expression, is the scalar quantity (energy or species concentration), and 􀀀 is a parameter that describes the diffusive velocity of the scalar quantity. For energy, this would be the thermal diffusivity, while for species balances, this would be molecular diffusivity. The quantity q is the sink or source term for the scalar quantity. For species balances this is the term that describes the consumption or generation of a chemical species from a reaction. These equations form the general model needed to describe a combustion system. Whether written in differential form or integral form, numerical techniques have been developed to solve these equations for a variety of systems. The actual computation of pertinent properties from these models is too labor intensive to do by hand, making computation ideal for the solution of these equations for a system of interest. Even with computers, solving these equations for any general system is not without problems. One prominent issue in the field of CFD is the modeling of turbulent flow regimes. Examination of the momentum balance equation (Equation 1.2) shows primarily two major forces that influence fluid flow: inertial forces and viscous forces. A dimensionless quantity that gages the relative importance of inertial forces to viscous forces is called the Reynolds number, and it can be defined a number ways depending on the physical system of interest. When the inertial forces are small relative to the viscous forces (low Reynolds number flow), the resulting flow field is relatively simple and can be easily computed for most systems. When the inertial forces overwhelm the viscous forces (high Reynolds number flows) the character of the flow field quickly becomes complicated. Ferziger and Peric (2002) described the character of turbulent with the following observations: Turbulent flows are highly unsteady. Flow velocities fluctuate rapidly in all three dimensions. These flows contain a significant amount of vorticity. Turbulence increases the rate at which scalar quantities are mixed. Turbulent flows exhibit a wide range of temporal and spatial length scales. This last property of turbulent flows is especially troubling for simulation. Turbulent flows contain eddys and flow characteristics that span a wide range of length scales, and the higher the Reynolds number, the larger the range of lengths scales. In such flow systems, in order to capture all the length scales in the simulation, the physical domain must use a sufficiently small mesh resolution. As the Reynolds number increases, the 5 needed mesh resolution becomes so small that the computational resources become quickly overwhelmed. Even with modern computing capabilities, there are strict limitations in the ability to simulate turbulent flows using the standard Navier-Stokes equations. Using the Navier-Stokes equations to simulate flow fields is called Direct Numerical Simulation (DNS), and while it is the most rigorous among the common models for simulating flows, it is also the most computationally expensive. With current computational resources only turbulent flows with relatively low Reynolds numbers and simple flow geometries can be simulated using DNS. Instead of solving for the exact flow fields, the flow velocities can be averaged over a certain time period to obtain a time-averaged flow field. Such a method averages out all eddys common to turbulent flows in the flow field and uses special models, called subgrid scale models, to estimate the effects of turbulent eddys on the average flow field. This approach calculates the large scale behavior of the flow, but largely ignores smaller scale flows that occurs in turbulence. This approach is called the Reynolds-Averaged Navier- Stokes Equations (RANS). In terms of detail captured in the flow and the computational expense it is the opposite of DNS. RANS allows solutions of highly turbulent flows, and for many physical situations it captures all the needed physics to accomplish an analysis. For example, if one is interested in capturing the overall flow direction and magnitude, the average force of the fluid on a solid body, the degree of mixing between two fluid streams, or the amount of substance reacted RANS can be useful. RANS, however, has its limitations: the effects of small scale flows and eddys is not perfectly modeled by subgrid scale models, and if more detailed information is needed about a flow, then RANS will not suffice. Another method for simulating turbulent flow that is a middle ground between RANS and DNS in terms of computational expense and predictive rigor is Large Eddy Simulation (LES). Traditionally, meteorologists have applied LES for weather prediction. Instead of averaging all secondary flows, LES resolves larger scale flows and eddys while averaging smaller scale fluid structures and using subgrid scale models to simulate their effects on the flow field. LES allows simulations to capture some of the details of turbulent flows without overloading computational resource. The development of methods like RANS and LES has greatly expanded the capabilities of CFD to simulate and predict the properties 6 of turbulent flow systems. 1.3 Pool Fires A combustion reaction requires mainly three components: (1) a fuel, (2) an oxidizer (usually oxygen), and (3) a sufficiently strong heat source to ignite the reaction. Fuels can be any of a number of chemical species. Most fuels are primarily composed of carbon (hydrogen gas being the most common exception.) Fuels can be solid, liquid, or gas, but combustion is a gas phase reaction. Gas fuels can burn as soon as all other conditions for the reaction are met, but liquids and solids must experience a change to the gas phase first before combustion can occur. Liquids must be vaporized to the gas phase before they can burn. Some solid fuels can sublime directly to the gas phase, but the most common mechanism for solid fuels to convert to gas phase is through chemical decomposition of the solid fuel into gas phase products. This process is called pyrolysis. There are safety issues to be studied from fires that result from the burning of gases (i.e., natural gas pipeline leak) and solids (i.e., forest fires), but military and industrial groups are especially interested in the effects of liquid fires. As seen the example mentioned at the start of this chapter, great damage to property and life can occur from liquid fuel spills. Transportation accidents and fuel spills at industrial sites are the types of accident scenarios that concern these groups. For example, if an aircraft crashes and spills its fuel and the fuel should ignite, it is of interest to find out what the potential damages and other effects of the fire might be. If a piece of military ordinance were to be engulfed in the resulting flame, it is of interest to determine if that explosive would detonate and how long it would take. It is also of interest to know if such a fire were to occur how close a person could stand to the flame and for how long before the individual experiences burns or if they would burst into flames immediately. Researchers are also interested to know if a fuel spill occurs, how far it would spread. Since most spills occur on grass, dirt, or other porous ground, the absorption of the fuel into the ground would affect how far across the ground the fuel and the fire would spread. These types of liquid fires where liquid fuel is spilled and ignited are called pool fires, and they are frequently studied. Researchers are interested in studying the way these fires 7 behave under different conditions. For example, the size of the pool can affect the flow regime (laminar or turbulent) of the flame, the height of the flame, the dominant modes of heat transfer from the flame, and the intensity of the heat output of the flame. The presence of crosswind can also have a significant impact on the behavior of the flame. Researchers often use metal devices equipped with thermocouples which they place in or near the pool fire in order to measure the heat input to the device. These devices are placed in different areas of the pool to measure the heat output from the flame in different region of the pool. These devices are called calorimeters. Another issue of interest in the study of pool fires is the rate at which the fuel burns. Researchers use devices such as thermocouple rakes, pressure transducers, or they can design the pool system to resupply fuel to the pool such that the fuel level remains steady and the burn rate can be inferred from the mass replenishment rate. Fire experiments have been conducted on pools as small as a few centimeters in diameter to as large as several meters in diameter, and like most fire experiments they can be quite costly. Therefore, the modeling of pool fires with computers using CFD is also widely used. Computational models, when adequately developed, can be a powerful tool in understanding and predicting the behavior of pool fires without the cost of experiment. ARCHES is an example of such a CFD code developed by the research team at the Center for the Simulation of Accidental Fires and Explosions (C-SAFE) at the University of Utah. According to Spinti et al. (2006), ARCHES uses LES and a finite volume scheme to solve the conservative relations for reactive flows. ARCHES is built upon a computational framework code in C++ called Uintah. Uintah enables the use of massive parallelization for computational codes like ARCHES. With this framework in place, ARCHES can run simulations using thousands of processors. ARCHES has been utilized for a variety of combustion-related systems like pool fires, flares, helium plumes, and so forth. It also employs discrete-ordinate methods to calculate the radiative heat flux generated in the fire. This feature is especially important for calculating the heat flux from the flame to an immersed or adjacent object. 8 1.4 Research Objectives 1.4.1 Objective 1: Boundary Conditions Computational codes like ARCHES take some variant of the Navier-Stokes equations and discretizes them spatially and temporally. The differential or integral equations become algebraic equations that must be solved for a discretized, three-dimensional domain. A numbers of issues can arise when working with computational domains in codes like ARCHES. The grid must be fine enough to capture the important physics of interest in the physical system as well as the important flow structures, but if the mesh is too fine it can get computationally prohibitive. Also stability issues arise with mesh size. For example, Courant stability conditions require that the temporal step size must not be too large, and the smaller the spatial step size the smaller the time step must be to keep the simulation numerically stable. An important factor that affects the stability of the computational domain and the accuracy of the predicted data is the use of accurate boundary conditions. Examination of the differential forms of the Navier-Stokes equations (Equations 1.1 and 1.2) show that these are partial differential equations involving spatial derivatives. Any differential equation with spatial derivatives requires boundary conditions for the solution of that equation on a physical domain. For an ordinary differential equation with a spatial derivative, the boundary condition affects the values but not the shape of the function over the domain of interest. For partial differential equations like the Navier-Stokes equations the boundary conditions become even more important, especially in a three-dimensional domain. The boundary conditions are functions in and of themselves that determine property values at the edges of the computational domain. The values of the boundaries can influence the entire character of the solution of the domain in both value and character. In other words, a change in boundary condition can radically change the character of the entire solution. Thus, in order to obtain accurate information about a physical system such as a pool fire it is important to have accurate boundary conditions. CFD codes like ARCHES employ different types of boundary conditions. Some examples include boundaries where fluid velocities, fluid pressures, or temperatures are specified (Dirichlet boundary conditions), and boundaries where the profile of quantities like temperature, velocities, and pressures 9 are specified (i.e., Neumann boundary conditions.) An important boundary condition employed in ARCHES and other fire codes that has been a point of weakness in the simulation of liquid pool fires is the inlet boundary condition for the fuel supply to the fire. This type of condition specifies the gas velocity into the domain, and it is not difficult to understand why such a quantity is so important to the accuracy of the fire simulation. The fire depends on its fuel supply in order to burn at all, and the amount of fuel supplied to the flames will influence all its properties. For fires where the fuel is a gas, the boundary is not difficult to specify. One simply needs to know the gas flow rate supplying the flame and program that profile into the inlet boundary condition. However, for liquid and solid fuels the situation is quite different. As already stated, liquid and solid fuels must convert to the gas phase by some process first before they can burn, and obtaining the rate at which the gas fuel feeds the flame requires an understanding of the phase-changing process. The focus of this project is the behavior of pool fires, so only liquid fuels are considered from here on. In the past, when modeling pool fires, ARCHES would create an inlet boundary at the bottom of the domain to represent the liquid pool. Data from similar experiments are used to obtain an average fuel burn rate for the pool fire, and from that average burn rate a fuel velocity is assigned to each boundary node where the pool is represented. For the entire simulation of the pool fire, that fuel velocity is used for the whole pool domain. In some cases, a ramping effect is applied to the inlet boundary condition so that the fuel velocity starts at a lower value and as the simulation continues the inlet velocity increases to the predetermined value based on experiment. This ramping is done to simulate the effect of the pool vaporizing more slowly at first before the liquid heats up and vaporizing more rapidly as the pool heats to a steady value. This approach to the inlet condition assumes that the pool vaporizes fuel uniformly over the whole area of the pool and assumes a constant average burn rate for the duration of the burn. This approach is easier to implement in a fire code, but the physical reality is quite different from this model. In reality, there is a more complex feedback relationship between the pool and the fire domain above the pool that affects the rate at which the fuel burns. At the point of ignition, the pool, which contains a mixture of volatile hydrocarbons, is evaporating fuel 10 at a certain rate and feeding that fuel to the flame. As the flame grows, it transfers heat to the surroundings through the various modes of heat transfer including back to the surface of the pool. The pool absorbs the heat and becomes warmer. As it warms the rate at which the fuel vaporizes increases feeding fuel to the flame to a greater degree. Eventually a steady temperature profile in the pool is reached as the heat input is balanced with the heat loss from vaporization. At that point the mass burn rate becomes steady as well. Another complexity of this situation is that the heat input to the surface of the pool is not constant over time or over the area of the pool, and the surface temperature of the pool is not uniform. Because of this the rate of fuel supplied to the flame will also not be uniform over the surface of the pool. The objective of this project is to more accurately predict the behavior of this type of inlet boundary condition by developing a mathematical model of the liquid pool. This new model allows for a boundary condition that responds to input from the computational domain the same way a liquid pool responds to the fire above it. This type of boundary condition is called a responsive boundary. As computational resource is always an issue in CFD, the responsive boundary model must not be too expensive in terms of computer resource. The physics present in a liquid pool are complex and assumptions must be made to produce an effective model. At the same time sufficient physics of the physical system must be captured to properly predict the right fuel burn rate without including any unnecessary complexity that would make the model a burden to computer resource. The primary purpose of the responsive boundary is to give an accurate fuel burn rate given the heat input. The estimation of the burn rate includes a mass transfer model for volatile species. Vapor-liquid equilibrium (VLE) is important for this system, and its model requires a VLE model. Because the vaporization rate depends on the temperature of the liquid it is important to model to some degree the temperature profile in the liquid pool. Another complexity to consider is that the pool loses mass as it vaporizes fuel. Thus, the physical domain of the liquid pool will shrink with time. The hottest layers of liquid at the top will vaporize away, affecting the temperature profile. The size of the pool will be an important factor in determining the behavior of the pool's burn rate. The presence of a crosswind over the pool is important and will affect the mode of mass transfer that 11 governs the vaporization rate of the pool (i.e., buoyancy driven flow or forced convection flow.) Another complexity to consider is the composition of the fuel. Different fuels will produce different flames with different behaviors. Heavier fuels will produce different burn rates than lighter fuels. Fuels that generate large quantities of soot in the flames with have different heat transfer properties that affect the burn rate than fuel with low soot potential. Several accident scenarios of interest involve the spilling of jet fuel. The common fuel considered is called JP-8. The problem with gasoline, jet fuel, and other common fuels is that they are complex mixtures of hundreds of hydrocarbon fuels and conditioning agents that can vary in composition according to time and location of where they are processed. The best way to treat this complexity is to model the behavior of the complex fuel using a simpler, surrogate mixture. A formulator of a surrogate fuel seeks to mimic certain properties of the complex fuel with a fuel of simpler, known composition. Eddings et al. (2005) and Violi et al. (2002) produce an example of such a formulation. They came up with two surrogates each of which consisted of six components to simulate certain properties of JP-8 such as smoke point, flash point, latent heat of vaporization, and heat of combustion. Modeling multicomponent fuel with hundreds of components whose identity and relative concentration are not fully known is impossible to program into the Responsive Boundary model, but a simpler, six component mixture with known composition is much more feasible. The goal for the project is to develop the Responsive Boundary model that can capture the important physics of the liquid pool and be able to adequately handle any fuel mixture of interest. The model must be incorporated into ARCHES to be used with pool fire simulations. Once incorporated into the CFD code it will be of interest to see the impact of the new boundary condition on the predictions of the pool fire's properties and behavior. 1.4.2 Objective 2: Verification and Validation In his brief history of the development of CFD, Roache (1998) notes that for a sub-stantial period of time when computer technology experienced tremendous growth and the various fields of computational physics (including CFD) also grew in like manner, the virtually single-minded focus of computationalists was centered on development of 12 computational technology to describe more and more complex physical systems, and very little was done to develop the means of quantifying the accuracy of results generated from new computational technologies. For a time, most computational results were accepted if the code compiled without error, the results seemed to make sense, and the data produced gave a good match to experimental data. Roache notes that although some groups gave proper attention to the quality of their code, large numbers of other codes developed suffered from a lack of accuracy in their results during this period. For example, in a study by Hatton (1997), over 100 scientific packages were analyzed over a period of four years. In one set of tests each code was checked line by line for what Hatton calls static faults. In this set of tests, a static fault is an error in the code that would not interfere with compilation or cause a crash upon execution of the code, but it could potentially lead to false results. In a second test, certain codes from one discipline (earth science in this case) were run using the same parameters and the same set of input data to compare the results among the different codes. To be brief, the test results showed the performance of the various codes to be problematic. The first set of tests showed that most codes were inundated with various coding faults, and the second set of tests revealed significant discrepancies among codes using the same computational procedures. What is perhaps most disturbing about these test results is that many of the codes analyzed were proven software. Meaning that they had already been in wide use. Computational science is a relative newcomer to the field of research along with the experimentalists and theorists. Although computational science has shown great promise for the benefit of research, the example above and other similar lessons in the history of computational science show that it cannot replace experimentation, and if its results are to be deserving of the same regard as those from experiment and theory, they must comply to the same standards of quality. Experimentalists must quantify the error in the results of their work for it to be properly recognized, and there is no reason that the same standard should not apply to the results that come of computation. Errors in computational models arise from the following sources: The first source is programmer error or coding bugs. As demonstrated by Hatton (1998) coding mistakes are an ever present and abundant source of error to a codes performance, especially in larger 13 codes. One can spend a significant amount of time and resource finding and eliminating bugs, and yet it seems that there are always more to find. Bugs that prevent compilation are relatively easy to resolve. Bugs that are not detected in compilation and still cause errors are particularly worrisome as their effects may not be apparent. The second source of error in a code is round-off error due to the limitations of finite-precision mathematics common to all computers. Beyond the utilization of stable algorithms, or algorithms that do not enhance the effect of round-off error in the course of their execution, little can be done to eliminate this type of error. As long as stable algorithms are employed in the code, the effect of round-off error is minimal. The third source of error in simulation is the error associated with spatial and temporal discretization of continuum equation models like the Navier-Stokes equations described earlier and the error inflicted from iterative procedures that are not sufficiently converged. The last type of error occurs due to choice of mathematical models that depart in some degree from physical reality due to simplifying assumptions. All but the last source of error represent discrepancies between the mathe-matical model of the system and the computer implementation of that model. These errors represent a problem with computer programming and algorithm development. The process of quantifying and hopefully minimizing such errors is called verification. The discrepancy between the computer implementation of the model and physical reality caused by the last of the sources of error mentioned above represents problems with the conceptual model. Quantifying this type of error in a code's performance is called validation. The terms verification and validation are given a more formal definition by the American Institute of Aeronautics and Astronautics (AIAA) (1998). They define verification as the process of determining that a model implementation accurately represents the developer's conceptual description of the model and the solution to the model. They likewise define validation as the process of determining the degree to which a model is an accurate representation of the real world from the perspective of the intended uses of the model. Trucano and Oberkampf (2002) note that both definitions qualify verification and validation as processes that are ongoing. The processes verification and validation are never complete. One can quantify error in a model for certain applications to a point, but one can never complete these processes for all possible applications. A code's performance is much like a the application 14 of a scientific theory, it cannot be proven, it can only be disproven. Nevertheless, a persuasive effort must be made to demonstrate the quality of code for relevant applications. A code must be adequately verified before it can be validated. These processes are necessary for a scientific code to achieve a certain credibility. Roache (1998) notes in his history of verification and validation development that several professional and scientific organizations changed policy in regard to the acceptance of scientific work which included numerical results from a scientific code. For example, in 1986 the ASME Journal of Fluids Engineering made the following declaration: The Journal of Fluids Engineering will not accept for publication any paper reporting the numerical solution of a fluids engineering problem that fails to address the task of systematic truncation error testing and accuracy estimation. Within ten years of this statement several other scholarly journals made similar policy statements. Just as experimental evidence must have error analysis to achieve credibility, so too must computational data. An objective of this research project is to take sufficient steps in the process of verifying the performance of the Responsive Boundary model and the validation of its results. As noted above, it may not be possible to prove the fidelity of the Responsive Boundary code, but steps can be taken to build reasonable confidence in its performance for the physical situations of interest. Figure 1.1 illustrates what is called a validation hierarchy. The hierarchy depicted demonstrates the complexities involved in the problem of predicting the total heat flux to an object immersed in a large transportation pool fire. The highest box in the hierarchy represents that very scenario. Moving down the hierarchy the overall problem is broken down into simpler physical phenomena. Each lower box represents a subset of important physical phenomena to be simulated. The higher in the validation hierarchy the more complex the system and the more difficult it is to obtain high fidelity experimental data for model validation purposes. The lower down the hierarchy the physical systems become simpler, and the experimental data available for such systems is higher in fidelity. It is important to validate computational models with the lower hierarchy systems first in order to improve fidelity with the higher systems in the hierarchy. The current project focuses on a subset of the hierarchy depicted in Figure 1.1. The 15 validation hierarchy for this project is shown in Figure 1.2. The peak of this smaller hierarchy is the problem of simulating a large liquid pool fire. The problem is broken into two parts. The first is improvement of the inlet boundary condition via development of the Responsive Boundary model. The second box represents validation of the ARCHES code through simulation of laminar helium plumes and collaboration of simulation results with experimental data from such plumes through an experimental technique called holographic interferometry. Helium plumes are excellent systems for validation of pool fires as the two systems have similar flow characteristics. Chapter 2 of this work establishes the important theoretical and experimental back-ground relating to pool fire research and identifies the important physics that influence the correct prediction of liquid pool burning rate, and it discusses previous attempts at liquid pool models. Chapter 2 also discusses common methods of verification, validation, and uncertainty quantification. Chapter 3 describes the formulation and application of the Responsive Boundary model. Chapter 4 describes verification and validation activities related to the Responsive Boundary model prior to its application with the ARCHES fire code. Chapter 5 describes the technique of holographic interferometry and the efforts to validate ARCHES calculations with holographic data from helium plume experiments. Chapter 6 describes verification and validation activities of the ARCHES code with the Responsive Boundary model incorporated. 16 Heat flux to a container in a 10-20m transportation fuel fire COMPLETE SYSTEM Heat transfer from large transportation fuel fires Fluid dynamics in CH4 fires O(1m) Heat transfer in or near transportation fires O( 1m) SUBSYSTEM CASES Momentum driven flames (Sandia TNF) Buoyancy driven flames (like Sandia TNF) Heat transfer with flow past complex geometry BENCHMARK CASES Non-reacting buoyant(He) plumes Reacting mixing layers (DNS data) Flow past complex geometry Radiation HT with complex geometry COUPLED PROBLEMS LES algorithm Subgrid turbulence model Subgrid mixing model Subgrid reaction model Radiation model Complex geometry model UNIT PROBLEMS Surrogate fuel formulation Gas phase chemical kinetic model Soot model with optical properties MOLECULAR PROCESSES Figure 1.1: The validation hierarchy for the problem of determining heat flux to a container engulfed in a large transportation pool fire. 17 Figure 1.2: A smaller hierarchy where the efforts of the present research are focused. CHAPTER 2 THEORETICAL BACKGROUND 2.1 Introduction In order to construct an effective model of a burning liquid pool it is essential to understand the physical system of the pool fire including the physical phenomena that influence the burn rate of the pool. With this in mind, a review of past research conducted with pool fires is appropriate. The primary objective of the Responsive Boundary model is to give accurate fuel evaporation predictions as boundary condition input to fire code simulations. As the literature is reviewed, the physical phenomena that most strongly affect the pool evaporation rate must be identified and distinguished from the physics that are less important to the this research objective. Several pool fire experiments in the literature seek to measure the evaporation rate of the liquid pool and determine the important physical factors that influence the burn rate. The researchers reasons for studying the evaporation rate is best understood in the light of safety concerns. In the scenario of an accidental fire, it is critical to know for the given conditions of the fire how the fire will spread, and it is important to be able to predict how much heat the fire will contribute to the surroundings and where the fire will distribute its thermal output. The burn rate of the pool is a critical factor in predicting these phenomena. According to Blanchat et al. (2006) the fuel vaporization rate is among the most important variable to be predicted in fire simulation as it determines how long the fire burns. Drysdale (1998) points out that in addition to the fire duration, the fuel vaporization rate is critical in predicting the size of the fire and the amount of heat released to the surroundings as he demonstrates in the following relation: Qc = m˙ Hc. (2.1) 19 In this relation, Qc is the heat release due to combustion of fuel, m˙ is the vaporization rate of the fuel, is an efficiency that represents the effect of incomplete combustion, and Hc is the heat of combustion for the burning fuel. Almost all the research on pool fires that measure the liquid vaporization rate focuses only on modeling the global burning rate of the pool. Several sources in the literature acknowledge that the vaporization rate varies spatially over the pool surface as well as with time, but as they are primarily interested in the overall heat output of the fire, the spatial variations are not as important to their purposes. While the prediction of heat output from a given accidental fire is the long-term goal, the immediate goal of this project is to improve the accuracy of fire code simulation by providing a more accurate inlet boundary condition, and this requires predicting the vaporization rate with the spatial and temporal variations intact. Such an improved boundary condition can conceivably increase the accuracy in the predictions of the behavior of the fire including the flame size and shape as well as the directional properties and intensities of the flame's heat fluxes. 2.2 Review of Pool Fire Research The history of pool fire research goes back at least as far as the 1950s where the first important mechanisms governing pool fires are identified, and it extends to the current time where large, costly experiments are performed with more modern, sophisticated instrumentation in order to provide more detailed and accurate measurements for the purposes of simulation validation. The following review of the research concerning pool fires is by no means exhaustive, but it does include a good, representative outline of the important experiments and findings that have occurred over the past 60 years. In addition to the literature cited here, other good reviews of the progress of pool fire research can be found from Koseki (1999) and Joulain (1996 and 1998). In order for the literature to be viewed in the right context it is helpful to discuss some of the common experimental conditions for pool fires. One of the early realizations about pool fires burn rates is its dependence on the size of the pool usually characterized by the pool's diameter. Different mechanisms of heat transfer affect the burn rate, and the dominant mode of heat transfer is determined by the size of the pool. For the experiments mentioned 20 in the literature the size of the pool could be as small as a fraction of a centimeter to as large as several meters ( 30 meters) in diameter. The pools themselves are frequently contained in a vessel, pan, or other type of container. Some of the vessels are made from ceramic materials, others use stainless steel. For smaller pool fires, cooling water is run through the lower portion of the pan to control the size of the flames in the fires experiment. For larger pool experiments the same purpose is served by floating a relatively thin layer of fuel over a layer of water. In some of the experiments the fuel level in the pan was kept constant by feeding additional fuel to the pan from a reserve supply to replenish the evaporated fuel. Such experiments are called steady pool fire experiments. With other pool fires, experimentalists simply fill the vessel with a specified amount of fuel and allow the fuel to burn without replenishment until the fuel is exhausted. These types of experiments are referred to as transient pool fire experiments. Another important phenomenon that affects burn rate is the presence of crosswind. In some experiments it is desired to have minimal wind effects and great effort is made to ensure that no external air fluctuations occur during the experiment. In other cases the wind is produced artificially and controlled to give a desired wind velocity and direction. Yet in other cases, especially with larger pool fires, the experiments are conducted in an open, outdoor environment. In these cases the wind speed and direction are carefully measured to account for the winds effect on the pool fire. The first major collection of research on the nature of liquid pool fires was conducted by two Russian researchers: V.I. Blinov and G.N. Khudyakov (1957). Their work was later reviewed by Hottel (1958) before their report was translated to English in 1961. Hottel calls attention to the importance of their work and derives an important relationship, based on their data and analysis, between the energy balance of the pool and the vaporization rate of the pool. The report by Blinov and Khudiakov details the results of experiments performed by themselves and others, and they identify important pool fire mechanisms and derive mathematical models to predict various behaviors of pool fires. They conduct numerous pool fire experiments ranging in size from less than a centimeter to nearly 23 meters in pan diameter. Their experiments include the burning of common industrial fuels such as gasoline, tractor kerosene, diesel oil, solar oil, and transformer oil. The author's report 21 includes findings on the size and shape of pool fire flames, the rate of pool vaporization versus the rate of combustion reaction in the flame, the behavior of flame pulsations and its relationship to the Reynold's number for pool fires, the different flow regimes (i.e., laminar, transition, and turbulent) of pool fires, temperature profiles and radiation properties of the flames, the phenomenon of soot formation, compositional changes in fuel mixtures during the burning process, the formation of what the authors call the homothermal layer and the phenomenon of boil over, the transient behavior of the fuel vaporization rate and its relationship to the pool diameter, the effect of fuel composition, oxygen concentration, wind speed, and fuel level with respect to the burn lip on the fuel vaporization rate, the variation of vaporization rate over the surface of the pool, the variation liquid temperature over the pool surface, and the vertical variation of temperature in a burning liquid. Frequently quoted by subsequent researchers, the work by Blinov and Khudiakov is widely considered to be foundational to the area of pool fire research. Contemporary to Blinov and Khudiakov is the work of Rasbash et al. (1956). The authors in this early and important work perform pool fire experiments with an alcohol mixture, benzole (an aromatic mixture), and petrol (gasoline) in pans that are 30 cen-timeters in diameter. The authors use thermocouples to measure the liquid temperature at and below the surface during the burning process. They observe the size and shape of the different flames, and note the difference in flame shape between the alcohol and other hydrocarbon fires. The authors are the first to describe the formation of the fuel vapor zone above the pool surface and how it changes during the different phases of burning and between the different types of fuel. They note that especially for the nonalcohol flames the dominance of radiation heat transfer to the pool surface over convection and conduction for 30-centimeter fires. They also give estimates of the radiation flux to the surface based on mathematical models and measurements of flame size, temperature, and emissivity. Burgess et al. (1961) perform a series of transient pool fire experiments. The fires range from 7 centimeters in diameter to 2.4 meters in diameter, and include fuels such as methanol, hexane, xylene, and what the authors call benzene (its likely that this fuel was actually benzole, an aromatic mixture.) The authors objective in this work is to corroborate the finding of Blinov and Khudyakov (1958) with regard to the dependence of 22 fuel burn rate on diameter and wind speed. The authors observe the transient warm up period and the steady state period of the pool burning process. They find that the steady burn rate reaches an asymptotic value once the diameter is sufficiently large, and they find that the wind speed increases the steady burn rate of the pool. Akita and Yumoto (1965) conduct pool fire experiments with methanol in concentric vessels ranging in size from 10 centimeters to 30 centimeters in diameter and in regular pans ranging from 1 centimeter to 60 centimeters. Unlike the experiments that Burgess et al. (1961) describe, these are steady experiments where fuel is supplied to the pan to keep the liquid level steady during the burning process. The authors find from the concentric ring pools that for the smaller fires ( 30 centimeters), the fuel burns fastest at the edge of the pool and the burn rate decreases as you move to the center of the pool. They also find that this pattern of burn rate is less prominent in larger pools. They also find that thermal radiation to the pool surface for small methanol fires can be neglected for the pools energy balance. They also confirm the validity for small pool fires of the mathematical model described by Hottel (1958) for predicting global pool burn rate. Thomas et al. (1965) perform experiments on larger (91-centimeter diameter) ethyl alcohol pool files. In this study, the authors are primarily interested in issues of air flow, air entrainment, and oxygen concentration in the flame region. However, they also measure heat flux to the pool surface for these larger fires. They estimate that at the center of the pool one fifth of the thermal heat flux is due to convection and the rest is radiation while at the edge of the pool convection and radiation share equally in the thermal input to the surface. Corlett and Fu (1966) study the effects of variation in liquid temperature, vessel wall conductance (thermal conductivity multiplied by wall thickness), and water contamination of the pool on the burn rate. The experiment includes pans ranging in size from 0.6 centimeters to 30 centimeters, and involves the burning of ethanol, methanol, and acetone. They find the effects of these three phenomena on mass burn rate to be negligible. What is perhaps more relevant to the present research is that they make 1 of the first attempts to measure radiation to the pool surface directly using a small insulated vessel containing fuel. The authors also note that radiation flux to the surface becomes important at 5 centimeters 23 to 10 centimeters diameter. They note that convection heat transfer dominates at the edge of the pool while radiation dominates in the center of the pool which is in agreement with other studies. Alger et al. (1979) make some very interesting observations concerning large (3.05 meter diameter), transient pool fire experiments that they conduct. They burn methanol and JP-5 (jet fuel) in separate experiments to contrast the behavior of luminous (JP-5) pool fire flames to that of nonluminous flames (methanol). Besides flame structure, the authors also seek to measure radiative feedback to the pool surface. The authors find that nonluminous flames produced higher flame temperature than that of luminous flames due to lower heat losses. Their measurements of radiation feedback indicated that for methanol the radiative input to the center of the pool surface was 75 to 80 kw/m2 while the JP-5 flame generated 100 kw/m2 in the same location. They estimate the convective flux to the surface to be about 8.3 kwm2 on average thus confirming the dominance of radiative feedback for large pool fires. What is also of great interest is that the authors comment on the optical properties of fuel pools. They find that the pool absorbs the thermal radiation effectively enough to only allow negligible penetration into the pool's depth. They estimate the penetration depth to be on the order of 1 centimeter. With regard to the reflectivity the radiative heat flux on the pool surface, the authors comment that most fuels have a refractive index between 1.4 and 2.0 leading to a rough estimation of pool reflectivity between 0.05 and 0.10. Shinotake et al. (1985) conduct transient experiments of moderate to large sized heptane pool fires (30 centimeters to 100 centimeters in diameter.) The authors measure radiation flux to the pool surface using Gardon type flux meters. In this study, the authors examine the transient behavior of radiation flux as the pool fire progresses. They note an overshoot in the radiative flux during the warm-up period of the fire experiment which they attribute to the formation of the fuel vapor zone that eventually blocks a portion of the radiation to the pool surface once established. According to the authors, this also explains why the feedback radiation tends to level off with increasing diameter while the radiation to the surroundings continues to rise with pool diameter. Klassen and Gore (1992) and Hamins et al. (1994) conduct a series of important pool 24 fire experiments with detailed description of the important phenomena (structure of flames, radiation feedback to the pool surface, burning rates, etc.) Their pool fires range in size from 7.1 centimeters to 1 meter using both simple and concentric ring burners. They burn a number of fuels, but much of their analysis focuses on methanol, heptane, and toluene as representative of nonsooting, moderately-sooting, and heavily-sooting flames, respectively. The authors measure flame properties such as flame temperature and soot formation for the soot forming flames. They also measure the optical properties of the flames (i.e., absorption and transmission of thermal radiation.) The authors are also interested in measuring the effect of turbulent motion in the flames on soot formation and temperature. Using narrow view radiative heat flux gauges they measure radiation input to the pool surface, and are able to measure angular dependence of the radiative input. They note for 30-centimeter fires that radiation flux is strongest at the center and declines toward the edge of the pool. The decline is more prominent for the methanol flames. They also note that radiation dominates the heat input for smaller pool diameters for toluene and heptane fires more than for those of methanol fires. They also note the presence of soot particles contaminating the pool surface during the burning process which could conceivably alter the optical properties of the pool. The authors also comment on the importance of the reflection of radiation in considering the pool's thermal balance. They also comment on the importance of re-radiation or thermal radiation originating from the pool surface. The data from this experiment is used to calibrate and validate models similar to the one being developed for the present research objective. Chatris et al. (2001) burn gasoline and diesel oil in pans of one, three, and four meters diameter. Their fire experiments are transient. Their objective is to measure the fuel burn rate as a function of pool diameter and wind velocity. They observe three distinct phases of transient burning: the transient warm-up phase, the steady burning phase, and the transient burn out phase. They report that the warm-up phase takes about 40 to 60 seconds for the fuels tested. They note that the phenomena of boil over is observed for gasoline and especially for diesel oil. They also note that the effect of wind on the burn rate is not significant until the wind speed reaches two m sec . Randsalu et al. (2004) conduct numerous JP-8 (another jet fuel) fires in 2-meter 25 diameter pans under conditions of 13 m sec wind. Their purpose is to measure fuel burn rate using a number of different experimental techniques. Their analysis focuses on the merits and disadvantages of each technique. Blanchat et al. (2006) perform four large-scale ( 8 meters in diameter), transient, JP-8, pool fire experiments in outdoor conditions at different wind conditions. Their objective is to obtain a variety of measurements for the purpose of aiding in the validation of computational pool fire models. Their measurements include flame and pool temper-atures, radiation flux to the pool and to the surroundings, and to immersed and nearby calorimeters. They also closely measure the wind conditions. Flame size and shape are monitored using cameras. Mass burn rate is also measured using a thermocouple rake. Brown et al. (2006) conduct a phenomenology and identification and ranking exercise (PIRT) to determine the important physics in pool fires that affect the fuel burn rate in preparation for the development of a liquid pool model similar to the one being developed for the current research project. The factors they considered in their analysis include radiation properties of the pool and of the flame region, the effects of fouling of the pool surface, the effects of fuel volatility and vapor pressure, convection within the pool, the effects of wind over the pool surface, the effects of the pools temperature profile, the thermodynamic properties of the fuel, the composition of the fuel, and the presence of materials near the fuel. The authors classify each phenomenon according to its importance in the determination of burn rate. It is also important to note that for many of the phenomena their effect on burn rate was not well understood. It is interesting to note how the objectives and the methods of pool fire research evolved over time. For example, in the earlier experiments the goal was to identify and gain a general understanding of the important mechanisms that control liquid fires. The researchers had relatively crude instrumentation and they could not take detailed measure-ment of physical properties in conditions of turbulence common to the larger pool fires. The earlier researchers could not directly measure radiation flux or soot concentrations. Many of the early observations made applied to the global behavior of the fire. They could describe the overall burn rate or the general shape, size, and appearance of the flame, but they could not immediately measure these same flame and pool properties 26 locally with the same certainty as with the global measurements. As time progressed, the instrumentation became more sophisticated and more detailed information about the physical properties could be measured. The objective of pool experimentation was no longer just about understanding the physics of fire. With developments in computational technology, computational prediction became another valuable tool in understanding fire behavior, and experimentalists then sought to measure more specific data in order to help develop, calibrate, and validate computer models. 2.3 Important Pool Fire Measurements As radiation flux has a very important influence on the rate of pool vaporization, especially in larger pool fires, it is worth reviewing some of the experimental methods employed to measure this quantity. Some of the earlier researchers such as Rasbash et al. (1956) infer the value of the radiation flux to the pool surface by measuring the the fuel depletion rate and employing simple global radiation models that depend on the flame's temperature and emissivity. Given the different sooting tendencies of the different fuels and the difficulty of measuring flame temperature accurately in turbulent flow conditions as well as the errors stemming from assumptions in the emissivity models such methods of estimating radiation flux are highly prone to error. The next technique is employed by Corlett and Fu (1966). In their experiment, they attempt to measure radiation flux to the pool surface by placing a small, insulated well in the pool at different locations. The well contains a portion of the fuel. The fire is ignited for a time and then extinguished. The level of fuel inside is measured before and after the burning period to determine how much fuel was burned. The radiation flux is calculated from an energy balance on the fuel in the well. Since the well is insulated, heat loss by conduction is considered negligible. One problem with this method is that both convective and radiative heat transfer cause the change in liquid level, and correlation must be used to estimate the convection heat transfer which brings substantial error to the calculation. This particular method can give measurement of radiation at different locations of the pool surface assuming the pool itself is sufficiently large to prevent flame disturbance from the well's presence, but it cannot measure instantaneous flux. Instead, it can only give a time average flux to the measured 27 point on the surface. In the studies conducted by Alger et al. (1979), Shinotake et al. (1985), and Hamins et al. (1994) the measurements of radiation flux to the pool surface are taken using devices that use Gardon-type sensing elements. The sensor in these devices is a thin foil which is connected to a sensor body at the edges and a thin wire at the center. The two connection points act as the hot and cold end of a thermocouple system. When heat flux is incident on the center of the foil a signal is generated that is proportional to the heat flux incident on the sensor. The Gardon-type sensor is usually water cooled to prevent heat conduction input to the sensor, and the device is built to withstand the high temperature environment of the flames. One significant problem with the sensor is that the incident heat flux includes both radiative and convective heat flux. A method must be found to separate the two types of flux in order to properly measure the radiative flux. In their experiments Alger et al. (1979) use a heat flux device with a sapphire window which allows radiant flux to pass but prevents the hot gases from entering the chamber and interfering with the sensor. The issue with this design is that the window itself could heat up and contribute its own radiative heat flux to the sensor. A different approach using the same sensor is employed by Shinotake et al. (1985). Their approach utilizes two sensors with the same construction except that one sensor surface is made black in order to absorb virtually all incident radiation, and the other sensor's surface is polished to give it a lower emissivity. As long as certain properties of each sensor are known it is possible to solve a small system of equations that yield the convective and radiative heat fluxes. Two problems with this approach are that the uncertainty in the measured fluxes are limited by the uncertainty in the measurements of the properties of the sensors, and the convective heat flux to the sensor's surface will be different from the convective flux to the surface of the pool as each surface has different properties that affect convection. Hamins et al. (1994) use a device with a small opening for radiative flux to enter. They also purge the opening by blowing nitrogen gas out the opening. The small opening allows the measurement of heat flux at different incident angles depending on the orientation of the placement of the gauge at the pool surface. The nitrogen purge prevents gas product from entering the gauge chamber and depositing material on the sensor. It also reduces convective flux to the sensor. In 28 their large pool fire experiments Blanchat et al. (2006) make use of a different instrument called a Heat Flux Gauge (HFG). The HFG is a well insulated, cylindrical device that uses a very thin metal plate with a thermocouple attached. The plate must be sufficiently thin such that there are only negligible thermal gradients in the plate. As the plate is exposed to the environment of the fire the temperature of the plate is measured. From the time data of the plate temperature the radiative heat flux is calculated from a heat balance model of the plate. The HFG was designed to measure steady-state radiative heat flux in a fire environment. An uncertainty analysis of the HFG by Blanchat et al. (2000) showed that in validation tests of the device uncertainty in radiative flux measurments could be as high as about 40 kw/m2. The authors identified the largest source of the uncertainty as unaccounted physics in the gauge's thermal model. The measurement of radiation flux is a difficult and ongoing processes. Examination of heat flux data from a turbulent fire reveals data that vary erratically with time. Any measurement of the flux will undoubtedly have large uncertainty. Fuel vaporization rate is another important quantity in pool fire experiments whose measurement is worth examining given that the focus of the present study to accurately predict this very quantity. It is worth noting that there are number of ways that the fuel burn rate is quantified. One way is to measure the liquid regression rate which is defined as the fall in liquid level with time and it employs units of length per time. The other way is to measure the change in fuel mass with time, and this is generally as the mass flux with units of mass per unit area per time. There are four techniques mentioned in the literature for determining how fast the fuel is burning. The first technique is visual inspection of the liquid level as it drops with time. This technique can also employ cameras to record the liquid level with time. Since the pool level is likely to fluctuate rapidly during the burning process it is more practical to connect a small glass meter to the pool whose level will be far more stable. This technique is best suited to transient pool fire experiments. For steady experiments where fuel replenishment keeps the pool level constant, the level in the reserve tank can also be monitored using this method. The next technique is to measure the mass of the pool or reserve fuel tank with time using load cells. Data of mass measurements with time can be used to calculate the mass burn rate from the slope of the data. Another 29 technique is to measure the liquid height with time by measuring the liquid pressure with pressure transducers place at the bottom of the pool. The last technique is an approach that has been developed more recently and used by Randsalu et al. (2004) and Blanchet et al. (2006). The approach uses an array of thermocouples commonly referred to as a thermocouple rake to measure the temperature of the fuel throughout its depth and the gas zone above the pool surface as the depth of the pool changes. Obviously, this approach is best suited to transient pool experiments. Since the temperature measured by the array rises sharply once above the pool surface it is simple to see the pool's surface position as a function of time from the temperature data. Randsalu et al. (2004) performed regression rate measurements using all four described techniques. They found the results for all the techniques to be comparable with the exception of the pressure transducer method. 2.4 The Pool Energy Balance In their classic work, Blinov and Khudyakov (1957) examine the evolution of the fuel in a pool fire. The fuel starts in the liquid phase, and as the fire begins to warm the pool the fuel then vaporizes into the gas phase. Once the fuel rises from the pool surface it mixes with the air, and once the fuel/air mixture is in the proper ratio the fuel reacts generating the proper chemical products. Blinov and Khudyakov are interested in determining how fast the fuel burns. They compare the rates of the different processes in the fuel's evolution and find that the vaporization rate is slow compared to the reaction rate of the combustion process. This means that the burning rate of the fuel can only go as fast as the pool supplies fuel to the flame zone through the process of fuel evaporation. The rate of combustion is also limited by the supply of oxygen to the flame. Blinov and Khudyahkov find that the rate of pool vaporization depends on the heat input to the pool surface. In his review of their data Hottel (1958) identifies three sources of heat transfer to the pool from the flame: Radiation from the flame, convection to the pool surface due to high temperature gases adjacent to the pool, and conduction to the pool through the heated experimental vessel in which the fuel is contained. The pool loses energy through the process of evaporation. Figure 2.1 shows a rough schematic of an experimental pool and demonstrates the three sources of heat input to the pool. 30 Also, in their experiments Blinov and Khudyakov measure the steady, liquid pool regression rate as function of the pool's diameter. They find that the steady regression rate is highest at small pool diameters and drops sharply with increasing diameter. The regression rate then flattens out to a minimum value (around 10 centimeters diameter for most fuels) and begins to rise again. The regression rate rises and then reaches an asymptotic value at a certain pool diameter that is generally above 1 meter diameter for most of the fuels tested. Figure 2.2 shows a qualitative graph of the regression rate with pool diameter based on the work of Hottel (1958). Note that in Figure 2.2, the curve varies in the critical lengths from fuel to fuel. Also note that the flow regime regions are labeled with the regression trend. As mentioned before the Reynold's number is what generally characterizes the flow regime of a given flow system. Its mathematical definition for a pool fire is: Re = u1l . (2.2) Here, Re is the symbol for the Reynold's number. u1 is the system velocity. For the pool fires the velocity is the fuel velocity as it leaves the pool. The symbol l represents some characteristic length that depends on the geometry of the system. For the pool fire system, the characteristic length is the pool's diameter. Lastly, represents the fluid kinematic viscosity. Although the Reynold's number traditionally represents the flow regime in the case of pool fires, Blinov and Khudyakov choose to represent the flow regime by the pool diameter alone. In their explanation of the regression rate trends, they claim that the different modes of heat transfer are dominant at different pool diameters, and that these regions of heat transfer control also correspond closely to the regions of flow regime. At small pool diameters, where the flame is laminar they argue that conduction from the pan is the dominant mode of heat transfer. In the region of large pool size ( 1 meter or larger in most cases) where the flame is fully turbulent, radiation is the dominant mode. Convection is more or less constant through the whole range of pool diameters, and the region between the two regions of conduction and radiation dominance is where the flow is in transition 31 to turbulence and the regression rate is at its lowest. Hottel (1958) supports the reasoning for this explanation of regression rates through a mathematical model of the pool's energy input: q A = k1 Tf − TB d + U Tf − TB + F Tf 4 − TB 4 1 − e− d . (2.3) In this relation, q is the thermal energy to the pool, A is the pools area. The right-hand side of the relation is the sum of three terms. The terms, going from left to right represent mathematical models for heat transfer due to conduction, convection, and radiation. In this part of the relation, d represents the pool's diameter, k1 is thermal conductivity, Tf and TB represent the flame and pool temperatures, respectively, U is the heat transfer coefficient for Newton's law of cooling, is the Stefan-Boltzman constant, F is a geometric view factor that represents the flames view of the pool surface, and is Beer's law extinction coefficient that models the flame opacity with flame thickness. Note that the convection term has no dependence on pool diameter. This supports the assertion that convection heat transfer remains constant through the range of pool diameters. The conduction term contains the pool diameter in its denominator, so when the pool diameter is small the the conduction term will be large and the term becomes smaller as diameter increases. This supports the observation from Blinov and Khudyakov that the conduction dominates heat transfer to the pool for small flames. As pool diameter increases the emissivity of the flame in the radiation term of Equation 2.3 approaches unity and the radiation term grows asymptotically to a maximum value. This confirms that radiation dominates heat transfer to the pool for large diameters, and it confirms that the regression rate will reach a maximum value as pool diameter grows larger. The dividing diameter between the different heat transfer zones is not uniform for all fuels. For example, Klassen and Gore (1992) found that for toluene fires thermal radiation dominated at diameters as small as 5 to 7 centimeters while for heptane this dominance begins at diameters of 20 to 28 centimeters. For methanol fires of 30 centimeters diameter radiation is important along with convection. The explanation for these differences has to 32 do with each fuel's ability to radiate heat when burning. This property will be reviewed in more detail later. It is clear that conduction from the pan loses its dominance rather quickly as diameter increases. Only for pools of 5 centimeters diameter or less is conduction an important effect. Accidental fires considered to be a threat to life or property will certainly be much larger than 5 centimeters. Alger et al. (1979) as well as Klassen and Gore (1992) state that convection is important only in moderately sized fires ( 20 to 100 centimeters), and that for all flames 1 meter in diameter or larger negligible error is inflicted if convection is ignored, and the error only declines as the size of the pool increases. Since most accidental fires are much larger that 1 meter radiation becomes the most important mode of heat transfer in the study of pool fires. Much more focus will be placed on the effects and properties of radiative heat transfer than for convection or conduction. For simulations of large, turbulent pool fires radiation is the only mode of heat transfer to the pool that needs to be considered. For the simulation of moderately sized pools convection should also be added, especially if the flames are nonluminous (non-soot forming). As the larger pools have a burn rate determined almost entirely by radiation input, a simple mathematical expression has been developed to give the global burn rate for such fire. Blinov and Khudiakov (1957) as well as Burgess et al. (1961) describe the model. If conduction and convection are neglected then the first two terms on the right-hand side of Equation 2.3 are dropped leaving only the third term. The first part of the radiation input term represents the maximum vaporization rate, and the second part of the term containing the pool diameter dependence is the emissivity of the pool. As stated before the larger the pool the closer the emissivity comes to unity. With these considerations the following simple model for large pool burn rate is proposed: v = v1 1 − e− d . (2.4) In this equation, v is the burn rate of the fuel expressed as the liquid regression rate, v1 is the maximum regression rate under conditions of a flame emissivity of unity. In both studies by Blinov and Khudyakov and by Burgess et al., the two parameters of Equation 33 2.4 (v1 and ) are experimentally determined for a number of fuels. 2.5 General Properties of Pool Flames Blinov and Khudyakov (1957) make some interesting observations about the size and shape of the flames arising from pool fires. They define the flame as the reaction region which separates the zone where there is oxidizer but no fuel from the region where there is fuel but no oxidizer. They comment that the size and shape of the flame are largely dependent on the size of the pool. For the smallest of pool diameters ( 10 millimeters or less) the flame has a well-defined conical shape that is fixed (no pulsations.) As the diameter increases the flame begins to exhibit longitudinal pulsations. The height of the flame fluctuates. As diameter further increases the flame begins to break up. Once the pool is larger than 15 centimeters turbulence starts to manifest in the motions of the flame. As to the size of the flame, as the diameter starts to increase from the smallest diameters the ratio of flame height to pool diameter increases sharply throughout the laminar region. As diameter continues to increase the growth in the ratio begins to flatten out. In the turbulent region the ratio remains virtually constant. Another important factor in the size and shape of the flames of pool fires is the fuel type. Hamins et al. (1994) burn different types of fuel in 30-centimeter pans. They compare the shape and character of flames from heptane, toluene, and methanol. These fuels are chosen because of their different sooting tendencies, and because the shape of the flames produced by these different fuels are markedly different. Hamins et al. describe the shape of methanol flames as unusual compared to that of the other fuels tested. They describe the steady flame as a series of thin, blue sheets starting from the edge of the pan and sweeping inward to the center of the pool in wave-like patterns. In contrast, they describe the heptane and toluene flames as turbulent with a cylindrical shape and flames that are bright yellow in color. The sooting tendency is the main reason for the difference in flame character described by Hamins et al. Soot formation is an important phenomena that influences the radiative properties of the flame and ultimately the burn rate of the pool as well as the shape and size of the flame. Turns (2000) describes the formation of soot as a gas phase reaction that 34 occurs for certain fuels at select temperatures at the low point in the flame. He describes the formation and destruction of soot in four steps. The first step is the formation of precursor species or the formation of polycyclic aromatic hydrocarbons (PAH) from the various fuel species. The second step is the particle inception step where small particles of critical size (several thousand atomic mass units) form due to chemical reaction and coagulation. The third step is the surface growth and particle agglomeration of the small soot particles as they are exposed to the fuel-rich environment. The last stage is particle oxidation. As the particles are exposed the oxidation part of the flame, usually in the top regions of the flame, they are destroyed through the oxidation process. Fuels that destroy all of their formed soot are termed "nonsooting." Any fire that is highly efficient in burning the fuel supply and converting it to carbon dioxide will be nonsooting. In pool fires, the flames are not typically so efficient, and sooting frequently occurs. Certain fuels tend to produce more soot that others. Turns ranks the fuels from lowest to highest sooting tendency in this order: alkanes, alkenes, alkynes, then aromatics. Pool fires involving these fuel are soot producing. Alcohol pool fires, in contrast, produce little or no soot, and since thermal radiation originates largely from soot particles alcohol fires generate less radiant heat. Klassen and Gore (1992) report from their measurements of radiation flux from heptane, toluene, and methanol flames in 30-centimeter pans that the radiation heat loss for methanol is about 0.2. The heat loss for heptane and toluene are about 0.3. Relatively hot soot particles are responsible for the bright, yellow character of luminous flames and are proficient at radiating heat to the surroundings. The more luminous a flame the greater the radiative heat release, including that to the pool surface. Lumi-nous, soot-forming fuels have greater heat feedback the pool surface which causes higher vaporization rates, which in turn leads to larger, more turbulent flames. Also, because luminous flames lose more heat to thermal radiation, their flame temperatures are lower than that of nonluminous flames as is confirmed experimentally by Rasbash et al. (1956) where they report that the flame temperature for the alcohol mixture is about 1200o C. The same measurements for kerosine and petrol are about 200o C lower than that of the alcohol flame, and the temperature for benzole, a mixture of aromatics which has a higher sooting tendency, is about 300o C lower than that of the alcohol flame. Also, Alger et al. 35 (1979) report from their 3-meter pool experiments that the measured flame temperature for methanol is about 200o C higher than that of JP-5. In their work with 30-centimeter fires Rasbash et al. (1956) make some relevant comments on the formation of the flame shapes for different types of fuels. At the beginning of the burn a thin sheet of flame originates from the pan's edge and slopes downward to touch the surface of the pool before sloping upward to form a cylindrical shape with diameter smaller than that of the pan. As the burn process continues, fuel evaporates from the surface at an increasing rate which pushes the flames away from the pool surface and forms a fuel rich zone between the pool surface and the flame. Figure 2.3 shows a sketch of the shape of flames near the pool at different pool fire stages as described by Rasbash et al. As shown in Figure 2.3(A), at the start of the burning process the flames can touch a substantial portion of the pool surface. For the alcohols tested in their study Rasbash et al. found that this flame shape held for the duration of the burn. Figures 2.3(B) and 2.3(C) illustrate what happens to more luminous flames as the burning continues. During the steady burning period the flames fluctuate between the shapes shown in B and C of Figure 2.3. This pattern is consistent with the behavior of the different types of fuels. The nonluminous alcohol flames radiate less heat to the pool surface and generate less vaporization of the fuel. The influx of fuel is not enough to push the flames far from the pool surface. However the luminous flames produced by the kersosine, petrol, and especially benzole generate enough fuel vaporization to form a larger vapor dome over the surface and push the flames much higher. The formation of the vapor dome over the pool surface is an important phenomenon as it can affect the volatility of the liquid fuel, the convection heat transfer to the pool surface, as well as the radiation heat transfer to the pool surface. 2.6 General Properties of the Liquid Pool In their measurements of pool regression rate with pool fires Burgess et al. (1961) note that after the fire starts there is a burning-in period where the burn rate accelerates before reaching a steady burning period where the regression of the liquid level is constant. This 36 behavior is consistent with other observations of burning liquid fuels. As the flames grow they heat the pool, and as the pool warms it gradually vaporizes more fuel until a steady state is reached. Chatris et al. (2001) also note this transient behavior in their experiments. They describe the transient burning process in three steps as follows: The first period is a transitory warm up phase. In this phase the flames spread over the fuel surface, and then the flames gradually increase in size as the pool warms. They note that for gasoline this stage lasts 40 to 50 seconds, and for diesel oil it takes about 60 seconds. The second period is a stationary period characterized by a fully developed fire with relatively constant burn rates. This stage ends when the fuel depletes, so the length of time for the stationary phase depends on the amount of fuel in the pool. The last stage is another transitory period where the flame size and burn rates gradually diminish until the fire extinguishes. A very important property of the liquid in pool fires is the temperature of the liquid. Blinov and Khudyakov (1957), Hottel (1958), Rasbash et al. (1956) all note that when a pool fire ignites and the flames heat the liquid pool the surface temperature eventually reaches a steady value that is usually just below the boiling point of the liquid. This is found to be true of single component fuels and mostly true of fuel mixtures. From their measurements of liquid pool temperature Blinov and Khudyakov find that the temperature profiles with liquid depth follow a similar pattern for all measured fuels. Figure 2.4 is a qualitative sketch of the common temperature profile. Blinov and Khudiakov also propose a simple mathematical model for the liquid tem-perature with depth: (T(z) − To) Ts − To = e−kz. (2.5) In Equation 2.5, T(z) is the liquid temperature as a function of liquid depth, z (z = 0 corresponds to the pool surface.) To is the nominal temperature or temperature of the surroundings, and Ts is the pool surface temperature. The last symbol, k, is a parameter that determines the shape of the temperature curve. Blinov and Khudyakov find that this parameter varies widely for different fuels. They also find this parameter varies with other physical properties such as the material of the pan in which the fire burns, the diameter 37 of the pan, and the wind speed. They also find that k can vary with time. The important detail is not so much the specific mathematical model or its parameter values, but the shape of the curve itself. Examination of Figure 2.4 shows that the heating of the liquid occurs in a small ( 1 centimeter) layer near the the surface. Blinov and Khudyakov largely account for the shape of the temperature through the thermal diffusivity of the liquid. Since the thermal diffusivities of hydrocarbon liquids are relatively small the temperature profile would be expected to drop sharply past the pool surface. Also, as mentioned already, Alger et al. (1979) find that the thermal radiation to the pool surface penetrates to a small depth of the liquid pool, thus heating only that part of the pool. Blinov and Khudyakov also report on the horizontal variations of the liquid tempera-ture. For 25-centimeter pool fires they find that the temperature is highest near the edge of the pool and decreases toward the center. This is expected because the flames come closest to the pool near the edge of the pan. Both convective and radiative heat fluxes would be high at the edge of the pool leading to higher temperatures there. For larger pools it is found that radiative heat flux becomes large at the center of the pool which leads to higher temperatures in that location as well. Blanchat et al. (2006) demonstrate this heat flux pattern with measurements they take from 8-meter pool fires. Another important property of the liquid pools is the composition of the fuel itself. Blinov and Khudyakov (1957) describe some of the important effects of composition in their report. Rasbash et al. (1956) report that for each of the mixtures burned in their experiments the measured boiling point of each fuel changed during the course of the experiment. This observation is common for experiments involving fuel mixtures, and it is an expected trend since mixtures tend to vaporize the light components first. As they deplete the lighter components from the liquid phase, the boiling point of the liquid rises. The magnitude of change in the boiling point during the pool fire depends on the components present. Some mixtures contain hundreds of components with a wide range of boiling points. Other mixture's components may have a relatively small range of boiling points. Rasbash et al. report that for an alcohol mixture the boiling point changed from 77o C to 79o C. Their report for benzole shows slightly larger boiling point change from 79o C to 84o C. Their data for kerosine and petrol demonstration much larger boiling point 38 changes (155o C to 277o C for kerosine and 30o C to 200o for petrol.) Besides the change in boiling point, Blinov and Khudyakov observe different mixing patterns in fuel mixtures as they burn. In some mixtures they note that the top layer of the pool is well mixed giving a uniform composition to the liquid in that layer. This is ascribed to mixing that occurs when the surface liquid is cooled somewhat by the process of evaporation. The cooled liquid is more dense causing it to mix into the immediate lower layers and causing the mixing pattern in the heated layer of the liquid pool. In other cases it was noted that mixing occurred throughout the entire liquid pool. This happens for mixtures where the density differences between the various components is large enough to cause circulation throughout the liquid. The last type of liquid behavior is the formation of what Blinov and Khudyakov call the homothermal layer. As already mentioned here, the surface temperature of burning liquids tends to come to a steady value that is slightly below the boiling point of the liquid. For some mixtures this is not true. The homothermal layer is a well mixed zone where boiling of lighter components occurs. Under certain conditions if the layer grows in size, boil over occurs. Blinov and Khudiakov describe the formation and propagation of the homothermal layer in their report. As the fuel mixture heats up, the temperature of the liquid is less than the temperature of the pan wall. If the pan wall temperature rises higher than the liquid temperature then lighter components at the bottom of the layer begin to boil near the wall. The boiling causes vigorous mixing in the layer which can convect heat to lower layers in the liquid. As it does so and as the temperature of the pan gets hotter at lower locations the homothermal layer spreads and boiling increases. If the fuel is situated on top of a layer of water the heat from the fuel will heat the water. Depending on the conditions of the water (purity and presence of nucleate forming material) the water can heat to its boiling point and even superheat beyond its boiling point. When the water can form steam bubbles, it can do so quite violently. The expulsion of water vapor from the pool can project burning fuel for large distances creating a severe safety hazard. As noted above, not all liquids can form homothermal layers or boil over. First, this can only occur with mixtures. Also, for the boiling to happen the mixture must have components with a sufficiently low boiling point ( 100o C). The presence of water in many fuels promotes this behavior. Windy 39 conditions can promote this phenomenon since the winds can deflect the flames in such a way as to immerse the pan and speed the process of heating at the pan wall. Water cooling of experimental pool pan when properly applied can suppress the heating of the pan and prevent boil over. 2.7 Properties of Pool Fire Radiation and Convection As previously stated, most accidental fires are large and turbulent. This means that the dominant mode of heat transfer to the pools and thus the most important property to influence the pool vaporization is thermal radiation. This section, therefore, will address mostly properties of thermal radiation and only spend a minimal effort on convection. Thermal radiation is one of the three basic modes of heat transfer. According to Incr-opera and Dewitt (2002), unlike the modes of conduction and convection, the propagation of radiant heat does not require the presence of matter in the medium of propagation. Radiation is emitted from all matter though electromagnetic waves that are generated by the oscillations and transitions of electrons present in all matter. The molecular oscillations and electronic transitions are maintained by the internal energy and thus the temperature of matter. Thermal radiation is transmitted by electromagnetic waves of a certain range of wavelengths. Figure 2.5 is an illustration of the electromagnetic (EM) spectrum with the range of radiative heat transfer labeled. As is evident in Figure 2.5, radiative heat waves cover the visible range, a substantial portion of the ultraviolet range, and most of the infrared range. The wavelength of the emitted radiation depends on the molecular properties of the material from which it is emitted. Different molecular vibrations and oscillations as well as electronic transitions have different energies and emit waves at different wavelengths. In the pool fire system, the thermal radiation is emitted from two sources. The two sources are radiation emitted by optically active gases