ABSTRACT. A new scaling technique based on the hypothesis that flows in a compartment fire are

Transcription

1 ABSTRACT Title of Thesis: SCALE MODELING OF THE TRANSIENT BEHAVIOR OF HEAT FLUX IN ENCLOSURE FIRES Peter Surendran Veloo, Master of Science, 26 Directed By: John L. Bryan Chair Professor Jaes G. Quintiere Departent of Fire Protection Engineering A new scaling technique based on the hypothesis that flows in a copartent fire are buoyancy driven was introduced by Quintiere [4]. Based on this hypothesis, scaling relations for convective and radiative heat transfer within copartent fires is presented. A technique to easure and differentiate convective and radiative heat flux in copartent fires is presented which utilizes a newly developed etal plate sensor and Gardon heat flux gauge. Experients conducted to test the scaling hypotheses were conducted at two scales. Wood cribs were used to odel a fuel load. The repeatability of wood crib fires has been deonstrated. Experiental results indicate that radiation heat flux scales according to the therally thick eissivity criteria. Convective heat flux was deonstrated to scale with advected enthalpy. The convective heat transfer coefficient has been correlated against teperature rise within the copartent for both the before and after extinction cases.

2 SCALE MODELING OF THE TRANSIENT BEHAVIOR OF HEAT FLUX IN ENCLOSURE FIRES By Peter Surendran Veloo Thesis subitted to the Faculty of the Graduate School of the University of Maryland, College Park, in partial fulfillent of the requireents for the degree of Master of Science 26 Advisory Coittee: Professor Jaes G. Quintiere, Chair Professor Andre Marshall Professor Peter Sunderland

3 Copyright by Peter Surendran Veloo 26

4 To y other, father and brother. ii

5 Acknowledgeents I would like to thank the National Science Foundation for their financial support of this research. The copletion of this thesis would not have been possible without the guidance of y supervisor, entor and friend Dr. Jaes Quintiere. I a also greatly indebted to the support and constant encourageent I received fro the Fire Protection Engineering faculty and staff. I would especially like to thank y coittee ebers Dr. Peter Sunderland and Dr. Andre Marshall. I would also like to thank y fellow graduate students and colleagues at the Potoac Lab who were always willing to lend their support to y experiental and laboratory work. None of the experients in this thesis could have been successfully copleted without their help. I a especially grateful for the guidance and entoring I received fro Jonathan Perricone. I a also grateful to Yunyong Utiskul (Pock) who was always willing to lend e a hand throughout y tie at Maryland. I would also like to thank Ming Wang, Joe Panagiotou, Kyle Lehan and Tensei Mizukai for their support and help during the various stages of y research. Finally I would like to thank y parents whose support and encourageent ade it possible for e to pursue y graduate studies at Maryland. iii

6 Table of Contents List of Tables... vi List of Figures... vii Noenclature... x 1. INTRODUCTION Objectives Thesis Outline THEORY Diensionless Groups fro Conservation Equations Defining a Characteristic Tie and Velocity Diensionless Groups fro the Moentu Equation Diensionless Groups fro the Energy Equation Diensionless Groups fro Species Conservation Equation Suary of π Groups Scaling Relationships fro π Groups π 1 Reynolds Nuber π 2 Scaling Fire Power π 3 and π 4 Wall Material Scaling π 5 Convective Heat Flux Scaling π 6 Radiation Scaling Suary of Heat Flux Scaling π 8 Species Concentration Suary of Length Scaling Results Preserved π Groups Wood Crib Scaling Wood Crib Theory Derivation of Scaling for Crib Paraeters Derivation of Scaling for Crib Paraeters Croce and Heskestad MEASURING HEAT FLUX Previous Work on Convective Heat Flux Measureent Novel Sensor Design and Approach Calibrating Sensor Conduction Loss and Tie Response Corrected Sensor Output Sensor Tie Response in Copartent Fires EXPERIMENT DESIGN AND METHODOLOGY Design Requireents for Scaling Validation Experients Full Scale Crib and Vent Design Copartent Wall Material Design Proposed Testing Schedule Copartents and Sensor Setup Ignition of Wood Cribs RESULTS Prior Scaling Results and Data Coparisons Free Burn Results Copartent Burning Rate Data iv

7 5.1.3 Copartent Species Concentration Gas Teperature Data Repeatability Mass Loss Rate Repeatability Copartent Measured Convective and Radiative Flux Data Convective Heat Transfer Coefficient Scaling Results Gas Teperature Wall Teperature Radiation Convection Conduction / Total Heat Flux to Wall Analysis of Convective Heat Transfer Coefficient Data CONCLUSION REFERENCES v

8 List of Tables Table 2.1: Suary of π Paraeters Table 2.2: Suary of π Group Scaling Results Table 2.3: Typical Theral Resistor Quantities Table 2.4: Crib Paraeters Table 2.5: Crib Paraeter Scaling Relations Table 3.1: Suary of Unknown and Measured Variables Table 4.1: Final Large Crib Design Paraeters Table 4.2: Sall Large Crib Design Paraeters Table 4.3: Copartent Burn Testing Schedule Table 4.4: Suary of Copartent Diensions Table 4.5: Sensor Setup Coordinates Table 5.1: Perricone Test Identification vi

9 List of Figures Figure 2.1: Control Volue for Conservation of Mass... 4 Figure 2.2: Control Volue for Conservation of Moentu... 5 Figure 2.3: Control Volue for Conservation of Energy... 6 Figure 2.4: Circuit Analogy for Losses through Wall Surfaces Figure 2.5: Exaple Wood Crib Figure 2.6: Crib Porosity and Burning rate Experients by Croce [11] Figure 2.7: Plan View of Crib Figure 3.1: Metal Plate Technique to Measure Heat Flux [13] Figure 3.2: Metal Plate Sensor Figure 3.3: Built Plate Sensor Figure 3.4: Plate Sensor, Heat Flux Gauge and Therocouple Setup Vertical View Figure 3.5: Sensor Calibration Setup Figure 3.6: Conductive Losses fro Metal Plate Sensor as a Function of Incident Flux. 38 Figure 3.7: Metal Plate Sensor Conductive Heat Loss Coefficient Figure 3.8: Metal Plate Sensor Tie Response against Steady State Teperature Figure 3.9: Metal Plate Sensor Tie Response against Incident Flux Figure 3.1: Metal Plate Sensor Properties Calibration Results Figure 3.11: Sensor Measured and Corrected Response Sensor Figure 3.12: Sensor Measured and Corrected Response Sensor Figure 4.1: Burning Rate Behaviour of Cribs in Copartents [14]... 5 Figure 4.2: Burn Tie for Different Stick Thicknesses Figure 4.3: Scaled Wall Material Properties Plot against Gypsu Board Figure 4.4: Materials Scaled π 4 Group Copared to Gypsu Board Figure 4.5: 1/8 Scale Copartent Sensor Setup Figure 4.6: 1/8 Scale Copartent Sensor Setup - Rear View Diensions Figure 4.7: 1/8 Scale Copartent Sensor Setup - Top View Diensions Figure 4.8: 1/4 Scale Copartent Sensor Setup - Front View... 6 Figure 4.9: 1/4 Scale Sensor Setup - Diensions... 6 Figure 4.1: 1/4 Scale Sensor Setup - Diensions Figure 4.11: Coordinate Labelling Convention Figure 4.12: Sensor Setup - 1/8 Scale Copartent Figure 4.13: Left Wall, Ceiling and Back Wall Sensor Setup - 1/8 Scale Copartent. 63 Figure 4.14: Sensor Setup - 1/4 Scale Copartent Figure 4.15: Left and Ceiling Sensor Setup - 1/4 Scale Copartent Figure 4.16: Wood Crib and Pan Pre-Burn Setup Figure 5.1: Diensionless Free Burning Rate Results - Large Crib Design [3] Figure 5.2: Diensionless Free Burning Rate Results - Sall Crib Design [3] Figure 5.3: Diensionless Copartent Burning Rate Results - Large Crib Design [3] 69 Figure 5.4: Sall Crib Design, Upper Layer O 2 [3]... 7 Figure 5.5: Large Crib Design, Upper Layer O 2 [3]... 7 Figure 5.6: Data Coparison - 1/8 Scale Sall Fire (.44D,,.65H) Gas Teperature vii

10 Figure 5.7: Data Coparison - 1/8 Scale Sall Fire (.44D,.37W, H) Gas Teperature Figure 5.8: Data Coparison - 1/8 Scale Large Fire (.44D,,.65H) Gas Teperature Figure 5.9: Data Coparison - 1/8 Scale Large Fire (.44D,.37W, H) Gas Teperature Figure 5.1: Data Coparison - 1/4 Scale Sall Fire (.44D, W,.65H) Gas Teperature Figure 5.11: Data Coparison - 1/4 Scale Sall Fire (.44D,.37W, H) Gas Teperature Figure 5.12: Data Coparison - 1/4 Scale Large Fire (.44D, W,.65H) Gas Teperature Figure 5.13: Data Coparison - 1/4 Scale Large Fire (.44D,.37W, H) Gas Teperature Figure 5.14: Data Coparison - 1/4 Scale Sall Fire Mass Loss Rate Figure 5.15: Data Coparison - 1/4 Scale Large Fire Mass Loss Rate Figure 5.16: 1/8 Scale Sall Fire (.55D, W,.65H) Measured Heat Flux... 8 Figure 5.17: 1/4 Scale Sall Fire - (.44D, W,.65H) Measured Heat Flux... 8 Figure 5.18: 1/4 Scale Large Fire - (.44D,.37W, H) Measured Heat Flux Figure 5.19: 1/8 Scale Sall Fire - (.55D, W,.65H) Convective Heat Transfer Coefficient Figure 5.2: 1/8 Scale Sall Fire - (,.55W,.2H) Convective Heat Transfer Coefficient Figure 5.21: 1/8 Scale Sall Fire - (.44D,.37W, H) Convective Heat Transfer Coefficient Figure 5.22: 1/4 Scale Sall Fire - (.44D,,.65H) Convective Heat Transfer Coefficient Figure 5.23: 1/4 Scale Sall Fire - (,.55W,.2H) Convective Heat Transfer Coefficient Figure 5.24: 1/4 Scale Sall Fire - (.44D,.37W, H) Convective Heat Transfer Coefficient Figure 5.25: 1/4 Scale Large Fire (,.55W,.2H) Convective Heat Transfer Coefficient Figure 5.26: 1/4 Scale Large Fire - (.44D,.37W, H) Convective Heat Transfer Coefficient Figure 5.27: Sall Fire - (.44D,,.65H) Scaled Gas Teperature Figure 5.28 Sall Fire - (,.55W,.2H) Scaled Gas Teperature Figure 5.29: Sall Fire - (.44D,.37W, H) Scaled Gas Teperature Figure 5.3: Large Fire (.44D,,.65H) Scaled Gas Teperature... 9 Figure 5.31: Large Fire (,.55W,.2H) Scaled Gas Teperature... 9 Figure 5.32: Large Fire (.44D,.37W, H) Scaled Gas Teperature Figure 5.33: Sall Fire (.44D,,.65H) Scaled Wall Teperature Figure 5.34: Sall Fire (,.55W,.2H) Scaled Wall Teperature Figure 5.35: Sall Fire (.44D,.37W, H) Scaled Wall Teperature Figure 5.36: Large Fire (.44D,,.65H) Scaled Wall Teperature Figure 5.37: Large Fire (,.55W,.2H) Scaled Wall Teperature viii

11 Figure 5.38: Large Fire (.44D,.37W, H) Scaled Wall Teperature Figure 5.39: Sall Fire (.44D,,.65H) Scaled Radiation to Wall Figure 5.4: Sall Fire (,.55W,.2H) Scaled Radiation to Wall Figure 5.41: Sall Fire (.44D,.37W, H) Scaled Radiation to Wall Figure 5.42: Sall Fire (.44D,,.65H) Scaled Convection to Wall Figure 5.43: Sall Fire (.44D,.37W, H) Scaled Radiation to Wall Figure 5.44: Sall Fire (.44D,,.65H) Scaled Total Heat Flux to Wall... 1 Figure 5.45: Sall Fire (,.55W,.2H) Scaled Total Heat Flux to Wall Figure 5.46: Sall Fire (.44D,.37W, H) Scaled Total Heat Flux to Wall Figure 5.47: 1/4 Scale Sall Fire Convective Heat Transfer Coefficient Before Extinction Figure 5.48: 1/4 Scale Large Fire Convective Heat Transfer Coefficient Before Extinction Figure 5.49: 1/8 Scale Sall Fire Convective Heat Transfer Coefficient After Extinction Figure 5.5: 1/4 Scale Sall Fire Convective Heat Transfer Coefficient After Extinction Figure 5.51: 1/4 Scale Large Fire Convective Heat Transfer Coefficient After Extinction Figure 5.52: Diensionless Convective Heat Transfer Coefficient Correlation with Teperature Rise Before Extinction Figure 5.53: Diensionless Convective Heat Transfer Coefficient Correlation with Teperature Rise After Extinction ix

12 Noenclature A A A A o s sl Area Copartent Vent Area Surface Area of Crib Surface Area of Soke Layer A w Surface Area of Copartent Walls b Wood Crib Stick Thickness C Wood Species Burning Rate Constant C.V. Control Volue C.S. Control Volue Surface Area c Specific Heat p D Copartent Depth d Wood Crib Stick Length F View Factor g Gravity Gr Grashof Nuber H Wood Crib Height H c, hc Heat of Cobustion h Copartent Vent Height h Convective Heat Transfer Coefficient c h, Metal Plate Sensor Calibration Convective Heat Transfer Coefficient c plate h * Diensionless Convective Heat Transfer Coefficient h Metal Plate Sensor Conductive Heat Transfer Coefficient k h eff Cobined Convective, Radiative and Conductive Heat Transfer Coefficients Calibration h eff, fire Cobined Convective, Radiative and Conductive Heat Transfer Coefficients Copartent Fire h, Copartent Wall Convective Heat Transfer Coefficient k w fire c Copartent Wall Material Conductivity k air Conductivity Air L Metal Plate Sensor Calibration Mount Length L e Mean Bea Length l Characteristic Length Copartent Height & Mass Flow Rate & Mass Loss Rate / Burning Rate of Wood Crib N n n f Nuber of Stick Layers in Wood Crib Nuber of Sticks per Layer in Wood Crib Unit Noral x

13 Nu Nusselt Nuber P Porosity Pr Prandtl Nuber p Pressure Q fire Fire Power Q inc Incident Heat Flux Q Metal Plate Sensor Measured Heat Flux Q crr Metal Plate Sensor Measured Heat Flux Corrected for Tie Response Q * Diensionless Fire Power, Zukoski Nuber q& losses Total Heat Flux Losses fro Copartent q& Heat Loss through Copartent Vent q& q& q& o c r w q w, r q w, c q w, k Convective Heat Flux Radiative Heat Flux Total Heat Loss through Copartent Walls & Net Radiative Flux to Copartent Wall & Net Convective Flux to Copartent Wall & Net Radiative conductive flux through Copartent Wall q& cond Conductive Losses fro Metal Plate Sensor & Total Radiative Flux fro Fire q fire, r q fire, c & Total Conductive Flux fro Fire q& HFG Heat Flux Gauge easured Heat Flux & Incident Panel Radiation during Metal Plate Sensor Calibration q inc, r q inc, fire & Incident Fire Heat Flux q & Heat Flux per Unit Area q & Incident Heat Flux per Unit Area inc q & Metal Plate Sensor Measured Heat Flux per Unit Area & Metal Plate Sensor Measured Heat Flux Corrected for Tie Response q, crr Re R r R k R r S s T T T c w sl Reynolds Nuber Effective Radiative Theral Resistance Effective Conductive Theral Resistance Effective Convective Theral Resistance Sensor Location Paraeter Control Volue Surface Area Wood Crib Stick Spacing Copartent Gas Teperature Wall Teperature Soke Layer Teperature xi

14 T Abient or Roo Teperature T ss Steady State Teperature T Teperature Metal Plate Sensor T d Vent Teperature t Tie ~ t Characteristic Tie tˆ Diensionless Tie t r Tie Response t, Measured Tie Response r t u u ~ û u a V W x Y y i i Sapling Period Flow Velocity Characteristic Velocity Diensionless Velocity Flow Velocity through Copartent Vent Volue Copartent Width Linear Distance Copartent Species Species Yield Greek α w Theral Diffusivity Wall Material α Absorptivity Metal Plate Sensor β Voluetric Theral Expansion Coefficient µ Dynaic Viscosity υ Kineatic Viscosity Π i, π i Diensionless Pi Group σ Stephan-Boltzann Constant ε Eissivity ε Eissivity of Soke Layer ε sl w Copartent Wall Material Eissivity ε HFG Heat Flux Gauge Eissivity ρ Density ρ Abient Density Γ Shear Stress τ Diensionless Tie δ Thickness δ Wall Material Thickness δ w t Theral Penetration Depth xii

15 1. INTRODUCTION Fro its use by the Wright brothers to odel and test designs for their flying achines, scale odeling has long been an iportant tool in engineering design and analysis. To date scale odeling can be found coonly utilized in the testing of prototype aircraft, autoobiles and structures. Scale odeling is especially appealing in its application to fire protection engineering due to the cost and space restrictions associated with laboratory based testing of full scale structures. There are a nuber of techniques currently used to scaling the fire proble including pressure odeling, Froude odeling and analog odeling. In pressure odeling π groups including the Reynolds nuber are preserved by varying the pressure of the abient at each scale [1]. Froude odeling on the other hand is conducted in abient conditions with the Froude nuber being the priary group preserved [2]. Analog odeling siulates the flow field through eploying the use of different fluids to siulate buoyancy effects. This thesis presents a novel technique of scaling the transient behavior of copartent fires through scaling tie with flow tie and velocity with flow velocity. The otivation in deriving this new technique to scale copartent fires is the deficiency in current scaling techniques to scale the transient behavior of copartent fire dynaics. This study is the second part of ongoing research using this novel scaling ethodology which was started by Jonathan Perricone [3]. Perricone presented a copelling arguent for the viability of this scaling ethodology by deonstrating its ability to scale the transient behavior of the burning rate of a designed fuel load, vent and copartent teperatures and species concentrations in copartent fires. The focus of ongoing 1

16 work using this scaling ethodology has been on scaling the transient response of structures within copartent fires. 1.1 Objectives Prior work conducted by Perricone [3], did not conclusively study how heat flux within the copartent fires was scaling. The objective of this study is to extend Perricone s work by investigating how heat flux has been scaled using the current scaling ethodology. Specifically, data needs to be collected on the convective, radiative and conductive heat transfer within enclosure fires. 1.2 Thesis Outline There are six chapters in this thesis. Chapter 2 presents the scaling theory including a coplete derivation of the diensionless π groups fro the governing equations. Theory is also present on the scaling of wood cribs which were used as the fuel load. Chapter 3 introduces a novel etal plate sensor which will be used with a Gardon heat flux gauge and therocouple to elucidate inforation about the convective and radiative heat fluxes in the copartent fires. A coprehensive theory of these etal plate sensors is presented along with their calibration procedure and results. In chapter 4 the experiental design and ethodology is presented. The experiental design procedure includes the copartent wall aterial and fuel load design. Sensor placeent is also presented along with the ignition ethodology for the wood cribs. Chapter 5 presents the results, analysis and discussion of the results obtained fro the experients. The final chapter provides a conclusion to this study. 2

17 2. THEORY Chapter 2 presents the theory underlying the scaling ethodology used in this study. First, the characteristic velocity, characteristic tie and π groups are derived. Fro these π groups the scaling relationships for convection, radiation and conduction within the copartent are derived. Finally the scaling theory is applied to wood cribs which are used to odel a fuel load within an enclosure. There are three ethods generally adopted for the derivation of the diensionless π groups necessary to perfor the siilitude scaling of a syste [4]. The first is the Buckingha Pi theore. The second involves deriving the coplete partial differential governing equations pertaining to a syste and aking the diensionless. The third technique identifies the governing physics of the proble in its siplest for. These siplified governing partial differential equations are then ade diensionless. The latter technique has been adopted in this chapter to derive the π groups necessary to scale copartent fires. Quintiere [4] outlines the developent of the coplete set of π groups necessary for the scaling of copartent fires using this technique and should be referred as a coprehensive resource. Chapter 2 expands on this outline by providing a coplete derivation of the π groups used in this study. A coplete list of all notation used in this and all following chapters is listed in the noenclature. 3

18 2.1 Diensionless Groups fro Conservation Equations Consider a control volue located in the fluid flow field of a copartent fire, as shown in Fig 2.1. V A u. Figure 2.1: Control Volue for Conservation of Mass The governing equation for the conservation of ass is derived fro the above control volue. The integral expression for conservation of ass within the control volue is [4]: C. S. d ρ ( u n ) da + ρdv = (2.1) dt C. V. If the flow within the control volue is assued to be steady, incopressible and onediensional the above governing equation for conservation of ass reduces to: & = ρua (2.2) A siilar control volue in the fluid flow field is used to derive the governing equation for conservation of oentu, Fig

19 u ΓS A. V ρgv Figure 2.2: Control Volue for Conservation of Moentu If an approxiate for of the one-diensional oentu equation in the vertical direction is considered the governing equation for oentu is [4]: du ρ V + u & ( ρ ρ) gv + pa + ΓS (2.3) dt Eq. 2.3 describes the relationship between the unsteady oentu and oentu advection to the buoyancy, pressure and shear forces respectively. Finally, for the derivation of the governing equation for the conservation of energy the sae procedure is adopted. The control volue is shown below in Fig 2.3. The control volue is setup around the interior of the copartent in-between the copartent walls and the abient. The copartent wall thickness is represented by δ w. The control volue is outlined with dashed lines. Flows in and out of the vent are assued to be constant and since ass flux fro the burning fuel is considered negligible these flows are then equal. The teperature ter T, is taken to be the gas teperature of the copartent. 5

20 V δ w Vent q& losses Q & fire T & T T w & Figure 2.3: Control Volue for Conservation of Energy The approxiate one-diensional governing equation for conservation of energy is: dt ρ c pv + c & p ( T T ) Q& fire q& losses (2.4) dt Eq. 2.4 equates the unsteady enthalpy ter and enthalpy advection to the energy release fro the fire and energy losses fro the control volue respectively. The approxiate for of the governing for species concentration within the control volue in Fig 2.3 is: dy & y Q& i i fire ρ V + Yi = (2.5) dt hc In Eq. 2.5, y i is the cheical yield, the ratio between the ass of species i and the ass of the reacted fuel. 6

21 2.1.1 Defining a Characteristic Tie and Velocity Fro the governing equations it is apparent that both a reference or characteristic velocity and tie are needed in order to ake the governing equations diensionless. They are derived by recognizing that the flows within the copartent are buoyancy driven flows. The proportionality of the oentu flux ter to the buoyancy force ter in Eq. 2.3 is exained giving: & u ~ ( ρ ρ )gv (2.6) Length scales, l, that will be adopted here and throughout the rest of this study refer to the characteristic length of the copartent, its height. Substituting Eq. 2.2 for the ass flow rate and revealing the length scales associated with each ter in Eq. 2.6 gives: ρu 2 l 2 3 ( ρ ρ) ~ gl (2.7) Rearranging the Eq. 2.7 gives: u ( gl) ρ ρ ρ ~ 1 / 2 1/ 2 (2.8) The characteristic velocity is defined as: ~ ρ ρ u = gl ρ 1/ 2 (2.9) In this study noralized variables will be denoted using a ^ and characteristic variables with a ~. The ideal gas law gives the following relationship: ( ρ ρ ) ( T T ) ρ = T (2.1) 7

22 Substituting Eq. 2.1 into the definition of the characteristic velocity, Eq. 2.9: 1/ 2 ~ T T u = gl (2.11) T An approxiate for of the characteristic velocity is then: ( ) 1/ 2 u ~ = gl (2.12) Exaining now the proportionality of the unsteady oentu ter and the buoyancy ter fro Eq. 2.3: ρv du dt ~ ( ρ ρ )gv (2.13) Making Eq diensionless using the characteristic velocity defined in Eq and revealing length scales associated with each ter: ρ ( gl) ~ t 1/ 2 duˆ dtˆ ~ ( ρ ρ )g (2.14) Rearranging Eq gives the definition for characteristic tie. An approxiate for of the characteristic tie is then: 1/ 2 ~ l t = (2.15) g 8

23 2.1.2 Diensionless Groups fro the Moentu Equation In order to ake the oentu equation diensionless the length scales associated with each ter ust first be revealed. After which, each variable is noralized with its corresponding characteristic variable and the shear stress ter is re-expressed as: du Γ = µ (2.16) dx This results in the diensionless governing equation for oentu: ˆ 2 du + uˆ dtˆ ( ρ ρ) ρ p µ + + ρl ρul ~ duˆ dxˆ (2.17) The first π group is fored fro the coefficient of the diensionless stress ter: Π µ ρul ~ 1 = 1 Re (2.18) This is the inverse of the failiar Reynolds nuber, Re, the ratio of inertial to viscous forces. If the exact for of the characteristic velocity is used as expressed in Eq. 2.11, this group can be rewritten in ters of the Grashof nuber, Gr: Π 1b = 1/ 2 T T T ν gl 3 1 Gr 1/ 2 (2.19) 9

24 2.1.3 Diensionless Groups fro the Energy Equation The sae procedure to ake the oentu equation diensionless is used to ake the energy equation diensionless. Teperature is noralized using abient teperature, Tˆ = T T. This results in the following diensionless governing equation for energy: dtˆ dtˆ + Q ( ˆ fire q& losses T 1) 1/ 2 5 / 2 1/ 2 5 / 2 ρ c p T & g l ρ c p T g l (2.2) The second π group is derived fro the diensionless source, or fire power ter: Π Q 2 * Q& = ρ c T g p fire l 1/ 2 5 / 2 (2.21) The second π group expresses the ratio of the energy released fro the fire to the enthalpy flow. It is also coonly referred to as the Zukoski a nuber, Q*. Heat lost fro the syste is a cobination of losses to solid surfaces, i.e. copartent walls and losses to the abient via the vent opening. These losses are represented below as q& w and q& o respectively. q & = q& + q& (2.22) losses o w Losses through the vent are expressed as the cobined radiation fro soke layer and copartent walls and can be approxiated using the equation: ( ε ( T T ) + ( ε )( T 4 ) q& = A σ T (2.23) o o sl 1 sl w In the above equationε sl is the eissivity of the soke layer and Convective losses fro the vent are negligible. A o the area of the vent. a Due to the popularization of its use in fire by Dr. Ed Zukoski 1

25 Heat lost fro the syste via the copartent walls can be expressed figuratively using a circuit analogy. q & w, c R c T Q & fire q & w, r Figure 2.4: Circuit Analogy for Losses through Wall Surfaces In the Fig 2.4 above, heat is transferred via the parallel paths of both convection and radiation to the copartent walls once released by the burning crib. This cobined heat flux is then conducted through the walls. & & (2.24) q w, k = q& w, r + q w, c R r Tw R k q & w, k T The radiation heat exchange between the soke layer and the wall can be expressed as a proble of radiation between two gray bodies. This proble is siplified by firstly assuing that the surface area of the soke layer and copartent walls is equivalent and secondly that the copartent copletely encloses the soke layer. The second assuption results in the view factor between the walls and the soke layer being unity. The general expression for this heat exchange is [5]: sl sl 4 4 ( T T ) sl w q& w, r = (2.25) 1 ε sl 1 1 ε w ε A σ + FA sl + ε A w w In Eq F, is the shape factor between the soke layer and wall. Using the siplifying assuptions above this reduces to: 11

26 4 4 ( T T ) σ sl w q& w, r = (2.26) ε ε sl w If the soke layer teperature is that of the copartent and the walls are considered to be covered in soot, Eq further reduces to: 4 4 ( T T ) q& = σε (2.27) w, r sl w The eissivity of the soke layer can be expressed as, [6]: ε sl e κl e = 1 (2.28) In Eq κ is the gas absorption coefficient and L e, the ean bea length of the gas. The ean bea length is a function of the gas volue shape [4]. Convective heat transfer to the walls is governed by: w, c c ( T T ) q& = h (2.29) w Conduction through the wall can be approxiated as conduction through a sei-infinite surface since the walls of the copartent will be designed using insulating aterials. Fourier s law for conduction can then be siplified: dt ( T T ) w q& w, k = k w = k w (2.3) dx δ w In Eq. 2.3 expression δ w represents the physical wall thickness. The physical wall thickness is scaled using the theral penetration depth for the case of a sei-infinite wall. Theral penetration is proportional to the square root of the wall diffusivity and tie [4], [5]: 1/ 2 1/ 4 ( ~ 1/ 2 k l δ t ~ α wt ) = (2.31) ρc g w 12

27 13 Substituting Eq into the diensionless loss ter of the energy equation gives: w o p w o losses q q l g T c q q q ˆ ˆ ˆ 2 5 / 2 / 1 & & & & & + = + = ρ (2.32) The diensionless wall loss ter in Eq is equivalent to the conduction losses through the wall aterial, Eq Substituting Eq. 2.3 into the diensionless wall loss ter then noralizing wall teperature with the abient and wall thickness with theral penetration depth, Eq. 2.31, gives: ( ) 2 5 / 2 1/, 1 ) / ( 1 ˆ ˆ l g T c T T Ak q p t w t w w w k = ρ δ δ δ & (2.33) Fro Eq the third and forth π groups are derived: ( ) 4 3, 1 ˆ ˆ Π Π = w w k T q& (2.34) In Eq the π 3 group is defined as: ( ) 4 3 / 4 1/ 2 1/ 2 5 / 2 1/ l g c c k l g T c T k l p w p t w = Π ρ ρ ρ δ (2.35) Fro Eq the π 4 is defined to be: 4 1/ 2 1/ 4 = Π g l c k w w t w ρ δ δ δ (2.36) Fro Eq the diensionless wall conduction loss ter, Eq. 2.33, can be expressed as the su of the diensionless convection and radiation heat flux to the walls. Therefore the diensionless convection heat transfer ter is: ( ) 2 1/ 2 1/, ˆ ˆ ˆ l g c T T h q p w c w c = ρ & (2.37)

28 The π 5 group is fored fro its coefficient: Π 5 h ρ c p c ( gl) 1/ 2 (2.38) The diensionless radiation flux is: 4 4 ( Tˆ T ) qˆ σε & o = (2.39) ρ 3 ˆ slt w 1/ 2 1/ 2 c p g l The coefficient fro Eq then gives the π 6 group: Π 6 σε T ρ c 3 sl 1/ 2 1/ 2 p g l (2.4) The eissivity of the soke layer provides the π 7 group which scales eissivity by preserving the absorbtivity and bea length. Π 7 κl e (2.41) Diensionless Groups fro Species Conservation Equation The species equation is ade diensionless through the sae procedure adopted for both the oentu and energy equations. Energy has is scaled by enthalpy flow. This gives the equation: ρ l l g 3 1/ 2 dyi dtˆ + ρ y Q * 2 5 / 2 ( ) 1/ 2 2 i gl l Y = ρ c T g 1/ l i h c p (2.42) Rearranging the above such that only the diensionless heat release rate is on the right hand side of the equation gives: h y c i p c T dyi hcyi + dτ c T y p i = Q * (2.43) 14

29 Eq. 2.43, the diensionless species equation, yields the final π group: hc Π 8 = (2.44) y c T i p Suary of π Groups Table 2.1 below suarizes the π groups entioned in this chapter and their corresponding fundaental relationship. Table 2.1: Suary of π Paraeters Π-Group Diensionless Relation Derived Relationship Π 1 µ 1 ~ = Moentu flux to ρ ul Re shear stress Π 2 Q& fire Fire power to 1/ 2 5 / 2 c T g l enthalpy flow ρ p Π 3 1/ 2 ( kρc) w 1/ 4 3 / 4 ρ c p g l Π 4 1/ 4 δ wg 1/ 2 1/ 4 α w l Π 5 Π 6 Π 7 Π 8 ρ c ρ c p h c σε T p ( gl) 1/ 2 sl 3 ( gl) 1/ 2 L e κ hc y c T i p Wall conduction losses to advected enthalpy Theral thickness to wall thickness Convective heat loss to advected enthalpy Heat loss to abient to advected enthalpy Absorption coefficient and bea length Cheical energy and i th species enthalpy 15

30 2.2 Scaling Relationships fro π Groups π 1 Reynolds Nuber The first π group is the inverse of the Reynolds nuber: Π µ µ = = ρ ul ρ g l 1 ~ 1/ 2 3 / 2 (2.45) Neither the abient density nor the dynaic viscosity of the fluid within the copartent is scaled in this study therefore this π group cannot be preserved. It is assued though that the flows within the copartent are turbulent, hence Re will be large and as a result this group becoes negligible π 2 Scaling Fire Power Scaling of the fire power between the odel,, and the prototype, p, by preserving the π 2 group: Π 2 Q& = ρ c T p 1/ 2 5 / 2 g l Q& p = ρ c T g p l 1/ 2 5 / 2 p (2.46) This results in the following relationship: 5 / 2 l p Q & = p Q& (2.47) l Eq states that in order to scale fire power fro the prototype to a scaled odel the fire power ust be scaled by the factor, ( ) 5 / 2 l p l. For the rest of this report this scaling factor will be siply referred to as 5 / 2 l. If in this case the odel were to be scaled geoetrically to be 1/1 th that of the prototype then the fire power would scale as ( 1) 5 /

31 As entioned previously, copartent teperature is noralized with the abient teperature. Since abient teperature is not scaled copartent gas and wall teperatures both scale to the zero power: T, Tw ~ l (2.48) π 3 and π 4 Wall Material Scaling π groups 3 and 4 describe how the wall aterial and its thickness should be scaled. π 3 states that: ( kρc) 1/ 2 w 1/ 4 3 / 4 3 / 2 ( kρc) Π 3 = w ~ l ρ c g l p (2.49) The π 3 group scales theral inertia of the wall aterial. Fro the π 4 group: δ g δ 1/ 4 w w 1/ 4 Π 4 = ~ l (2.5) 1/ 2 1/ 4 1/ 2 α w l α w The above group then states how the physical wall thickness and theral diffusivity of the wall aterial scale π 5 Convective Heat Flux Scaling The π 5 group scales the convective heat transfer coefficient: hc Π 5 = h ~ l 1/ 2 c c ρ p ( gl) 1/ 2 (2.51) There is an alternate eans of deriving a scaling relation for the convective heat transfer coefficient and that is through a turbulent forced flow boundary layer correlation [5]. This defines the Nusselt nuber and hence the convective coefficient as: 17

32 h c 4 / 5 1/ 3 Pr (2.52) l Nu =.37 Re k Substituting Eq for Re and assuing that Pr for the flow is unity gives an alternate scaling for the convective heat transfer coefficient: h c 2 5 ( gl) 1/ l 4 / k 1/ 5 ρ ~ hc ~ l µ l (2.53) π 6 Radiation Scaling Preserving the π 6 group scales eissivity and as a result also scales radiation: 3 σε slt Π 6 = ε ~ l 1/ 2 sl ρ c p ( gl) 1/ 2 (2.54) Using the approxiate odel for eissivity, Eq. 2.28, the scaling relation for eissivity can be rewritten as: ε sl κ e 1/ 2 = 1 e L ~ l (2.55) The gas layer can be either optically thick, κ >> 1, or optically thin, κ << 1. In the L e L e optically thick case the eissivity of the soke layer approaches unity. To scale the π 6 then requires: 3 σt Π 6 = T ~ l 1/ 2 ρ c p ( gl) 1/ 6 (2.56) This cannot be achieved since the abient teperature is not scaled, therefore the π 6 group cannot be preserved for the optically thick case. If the gas layer is optically thin then eissivity is proportional to the absorbtivity and bea length. The π 6 group then requires the following scaling: 18

33 Π σ ( Leκ ) T c ( gl) 3 ( lκ ) T ( gl) 3 6 = ~ κ ~ 1/ 2 1/ 2 ρ p ρ c p σ l 1/ 2 (2.57) The gas absorption coefficient varies with fuel, therefore by varying fuel type the gas absorption coefficient can be forced to scale to the negative half power and in doing so preserve the π 6 group Suary of Heat Flux Scaling Conduction is siplified using the linear for of Fourier s law, Eq Substituting wall thickness scaling, Eq. 2.5, into Eq. 2.3 gives: ( T T ) q& k = k w (2.58) α 1/ 2 1/ 4 w l Siplifying Eq results in wall conduction scaling with theral inertia: ( kρc) 1/ 2 w 1/ 4 q& k ~ (2.59) l Theral inertia is scaled by the π 3 group, Eq Substituting the scaling for theral inertia into Eq results in the scaling relation for wall conduction: q k 1/ 2 & (2.6) ~ l Convective heat flux scales according to the scaling relation for the convective coefficient used. Scaling using Eq results in convective heat flux scaling as: q c 1/ 5 & (2.61) ~ l Alternatively according to Eq. 2.51, convective heat flux scales as: q c 1/ 2 & (2.62) ~ l 19

34 Siilarly with convection, radiative heat transfer scales with eissivity. In the optically thick case eissivity approaches unity and fro Eq cannot be preserved, therefore radiation scales as: q r & (2.63) ~ l There are two approaches to scaling optically thin eissivity. The first approach varies the fuel and the second does not. If the fuel load is varied to force the gas absorption coefficient to scale by Eq then eissivity will scale to the half power. Therefore, for the optically thin case in which fuel is varied radiation scales as: q r 1/ 2 & (2.64) ~ l If the fuel is not varied then eissivity will scale as the ean bea length. Since the ean bea length scales to the unity power, radiation in this instance scales as: q r 1 & (2.65) ~ l π 8 Species Concentration The π 8 group scales species yield. Since none of the ters in the group are scaled yield then scales as: h y c i p c T y i ~ l (2.66) 2

35 2.2.8 Suary of Length Scaling Results Table 2.2 suarizes the scaling requireents for each π group. Table 2.2: Suary of π Group Scaling Results Π Group Quantity Scaled Coents T Teperature T ~ l Π 1 Π 2 Π 3 Π 4 Reynolds Nuber Fire Power Conduction Wall Thickness Not Explicitly Preserved 5 / 2 Q & ~ l 3 / 2 ( kρ c) ~ l α q& k δ w ~ 1/ 2 l w 1/ 4 ~ l 1 / 2 w 1/ 5 q& c ~ l Π 5 Convection 1/ 2 q& c ~ l Π 6 Π 7 Radiation Species q& r q& r q& r y i ~ l 1/ 2 ~ l 1 ~ l ~ l For siilitude between a prototype full scale enclosure fire and its scaled odel the dependent variables are a function of the following independent diensionless groups: T T g T, T w, u ( gl) xi t = function, l l g, y, 1 / 2 i 1/ 2 Π 1 7 (2.67) 21

36 2.2.9 Preserved π Groups It is not possible to preserve all the π groups derived previously. For exaple, the Reynolds nuber is not explicitly preserved. In order to preserve convection, the convective heat transfer coefficient needs to be scaled. The scaling theory then presents two contradictory ethods to scale the convective heat transfer coefficient. To preserve radiation requires knowledge of the gas layer eissivity. Herein lays the art of scaling, exaining the doinant physics of a proble and preserving the pertinent π groups. Fig 2.4 illustrates the circuit analogy for heat loss fro the copartent. A quantification of the circuit resistor quantities was given in [7] and [3] and is listed in Table 2.3 below. Table 2.3: Typical Theral Resistor Quantities Resistor Range ( 2 K/kW) Conduction 316 R Convection R c 1 Radiation R 15 Fro the Table 2.3 the conductive resistance is the ost doinant theral resistor. Designing the copartent walls using insulation board and blanket further increases k r this doinance. For this reason the π 3 and π 4 groups are preserved and the π 5, π 6, and π 7 groups discarded, i.e. conduction is preserved in favor of either convection or radiation. Eq is now odified to preserve the doinant physics: T T g T, T w, ( gl) u xi t, y Π Π Π 1 / 2 i function,, 1/ 2 2, 3, l l g 4 (2.68) 22

37 2.3 Wood Crib Scaling Wood cribs were chosen to represent a fuel load of furniture within the copartent. The wood cribs then had to be scaled according to the derived scaling relations. Fig 2.5 below shows an exaple of a wood crib and its associated variables. d Layers (N) Figure 2.5: Exaple Wood Crib s b b The variables for a crib have been suarized below in Table 2.4. Table 2.4: Crib Paraeters Crib Paraeter Sybol Physical Crib Property N Sticks per layer n Nuber of layers b Stick thickness d Stick length s Stick spacing Wood Crib Theory There has been extensive research into the burning rate of wood cribs. Notable work includes that of Gross [8] who discovered that the burning rate of various configurations of wood cribs can be grouped into two categories, either densely packed or openly packed cribs. Block [9] then defined a fundaental theory for the burning rate of either densely packed or openly packed cribs. He discovered that for densely packed cribs the 23

38 burning rate was a strong function of crib height and packing density whereas in the openly packed case it was a function only of the physical properties of the fuel eleents and not its geoetry. Block went on to define this openly packed burning rate as: Cb 1/ 2 & f = (2.69) In Eq. 2.69, C is a constant representing the species of wood [9]. Both Gross and Heskestad [1] referred to this dependency on stick density as the porosity factor: P A v 1/ 2 1/ 2 s b (2.7) A s An alternative view of porosity is as the ratio of vertical vent flow, 1/ 2 A v s, to the burning rate. Further work by Croce [11] shown below in Fig 2.6, clearly differentiates these two burning regies. In Fig 2.6 below, it can be seen that for porosity below.5 burning rate is dependent on porosity, this is defined as the densely packed wood crib burning regie. For porosities larger than.5 the burning rate is porosity independent and this is defined to be the openly packed burning regie. 24

39 Densely Packed Cribs Openly Packed Cribs Figure 2.6: Crib Porosity and Burning rate Experients by Croce [11] All wood cribs were designed in this study to all fall under the category of porosity independent or openly packed burning regies Derivation of Scaling for Crib Paraeters Fig 2.7 below is of a plan view of a wood crib. A v is the crib vent area: A v ( d nb) 2 = (2.71) Stick length can be expressed as a su of the stick thicknesses and the stick spaces: d = nb + ( n 1) s (2.72) Each crib variable can be expressed in ters of its scaling relations, i.e. d ~ l d ' or b ~ l b'. Using this technique of expressing the crib variables Eq can be rewritten as: d + d ' n' b' n' s' = nb + ( n 1) s l = l l l l (2.73) For Eq to be diensionally correct the following relationships ust be true: 25

40 d = n + b (2.74) d = n + s (2.75) It can be seen fro the two equations above that: b = s (2.76) Stick spacing s, can be expressed as: ( d ) nb s = (2.77) n 1 A v Figure 2.7: Plan View of Crib Fro the π 2 group, Eq. 2.21, fire power scales as: & 5 / 2 fire = & f hc ~ l (2.78) Q Substituting the equation for the burning rate of porosity independent wood cribs, Eq into Eq gives: 1/ 2 5 / 2 hc AsCb ~ l (2.79) 26

41 A s, in Eq. 2.79, is the surface area of the crib. Since the wood species used in this study is constant, neither hc or C in Eq can be scaled as they are constant. The total surface area of a crib is approxiated to be: A s ~ 4nNbd (2.8) Substituting Eq. 2.8 into Eq and reoving the constant ters gives: 1/ 2 5 / 2 nndb ~ l (2.81) Expressing Eq in ters of its diensional relationship gives the equation: b 5 n + N + d + 2 = (2.82) 2 Expressing porosity as the ratio of ass flow rate through vents to the burning rate gives: P A s & 1/ 2 v v = ~ (2.83) 1/ 2 Asb & f If porosity is then held constant between scales, air flow through the vents ust scale as the burning rate: 1/ 2 5 / 2 & ~ & f v = Av s ~ l (2.84) Substituting the expression for vent area and stick spacing derived above in Eq and Eq into the scaling relation for vent flows in Eq results in: s A v 1/ / 2 ( d nb) s 1/ ~ l = (2.85) Expressing Eq in ters of its length scaling relations as was done previously: s 5 2 d + = (2.86) 2 2 Since burn tie scales according to flow tie, burn tie will scale as: t f 1/ 2 b = ~ l (2.87) & f 27

42 Substituting in the scaling for burning rate and the expression for the total ass of a crib: nnb dρ 2 wood 5 / 2 l ~ l 1/ 2 (2.88) This results in the scaling relationship: 2 3 nnb d ~ l (2.89) This relationship expressed in ters of its scaling gives the equation: n + N + 2 b + d = 3 (2.9) Fro the stick length relationship, Eq. 2.72: d = n + b (2.91) There are therefore a total of four equations, Eq. 2.82, Eq. 2.86, Eq. 2.9 and Eq. 2.91, and four unknowns, n, N, b and d, which can now be solved to give the scaling relationship for each of the crib paraeters Derivation of Scaling for Crib Paraeters Croce and Heskestad Croce s scaling ethodology [7], based on Heskestad s hypothesis [6] is outlined in this section. Full equations have been expressed in ters of their length scaling relations as was done in Eq Croce [7] also preserved the Zukoski nuber, Eq. 2.21, and therefore had the sae scaling relationship for burning rate. Expressing this relationship as done previously in Eq gives: b 5 n + N + d + 2 = (2.92) 2 Preserving porosity between scales then gives: s 5 2 d + = (2.93)

43 Cribs were then designed to be geoetrically siilar, i.e. crib height and stick length were both scaled as l. Crib height relates to the nuber of layers and stick thickness as: Giving the equation: H = Nb ~ l (2.94) b + N = 1 (2.95) The stick length relationship, Eq and Eq. 2.75, gives the result: d = n + b (2.96) The geoetric scaling of stick length gives: d = 1 (2.97) Burn tie was not scaled according to flow tie as was done in the new scaling ethodology. There are now five equations, Eq. 2.92, Eq. 2.93, Eq. 2.95, Eq and Eq. 2.9 and four unknowns. This over-specified syste of equations is solved by relaxing the final equation. Table 2.5 below suarizes both the crib paraeter scaling relations fro Croce and that derived using the new scaling ethodology. Table 2.5: Crib Paraeter Scaling Relations Crib Paraeter Croce Flow Tie Scaling N l 5/8 l 5/6 n l 1/2 l 1/3 b l 1/2 l 1/3 d l 9/8 l 7/6 H l 1 l 2/3 29

44 3. MEASURING HEAT FLUX Chapter 2 discussed how heat flux scales in copartent fires. This discussion revealed contradictory ethods for the scaling of both radiation and convection. Knowledge of how heat flux scales is especially iportant in light of the further developent of this work to the scaling of structures within copartent fires. This chapter discusses the technique used in easuring and differentiating the different heat fluxes within a copartent fire. A brief discussion is given of previous ethods used to solve this proble. A novel technique of differentiating radiation and convection heat flux involving etal plate sensors is then introduced and given a rigorous theoretical treatent. 3.1 Previous Work on Convective Heat Flux Measureent Tanaka and Yaada [12] investigated the convective heat flux during the early stages of a fire and at extinction. By assuing that the flow into the copartent was unidirectional the energy equation could be siplified and the heat transfer calculated by easuring the heat release rate, flow rate through the opening and teperature of the flow. The for of the energy equation used was: d dt ( c p TV ) = Q& fire c ptd & Q& c ρ (3.1) In Eq. 3.1, Q & fire represents the energy released by the fire, Q & c, the convective loss coponent, T d, the teperature of the flow through the vent and &, the flow rate through 3

45 the opening. If V and c p ρt are assued to be virtually constant then Eq. 3.1 can be siplified to: Q& c = Q& c T & (3.2) fire p d Mass conservation is expressed as: d dt ( V ) = & ρ (3.3) Using the ideal gas law the ass conservation equation can be rewritten as: dt dt PMV = & (3.4) 2 RT The rate of convective heat loss can then be calculated by substituting Eq. 3.4 into Eq The heat transfer coefficient is then calculated using the equation: h c = ( T ) A T Q& w c (3.5) Average teperature is taken to be gas teperature and the wall teperature was easured using a series of plates attached to the copartent walls. Therocouples were welded to the unexposed faces of the plates and these teperatures were taken to be the wall teperature. The convective heat transfer coefficient was correlated with heat release rate giving [12]: ρ h 2. 1 = Q* c c p ( ) 1/ 2 2 / gl.8( Q*) Q* > 4. 1 (3.6) In the above expression Q* is the diensionless fire power or Zukoski nuber fro Eq The length scale l above refers to the characteristic length of the copartent which in this case is the copartent height. 31

46 More recently Tofilo et.al, [13], studied the effects of sootiness and heat release rate on heat transfer rates for a copartent fire. The radiative and convective coponents of the heat flux were differentiated and studied. They devised a technique, to extract this inforation, which utilized a etal plate ebedded in the surface of the wall aterial, as shown in Fig Figure 3.1: Metal Plate Technique to Measure Heat Flux [13] The energy balance for the etal plate is [13]: dts 4 4 q& inc = ρ cδ + q& cond + hc ( Ts T ) + σ ( Ts T ) (3.7) dt The conduction losses fro the plate, q & cond, can be easured using the therocouples placed at either side of the plate within the insulation and using a siple linear approxiation to the conduction equation. The unsteady teperature ter can be considered negligible since the etal plate is thin. The incident heat flux to the etal plate, q & inc, is easured by a Gardon type heat flux gauge placed near the plate. 32

47 3.2 Novel Sensor Design and Approach It was decided that a new sensor would be created to elucidate heat flux inforation fro the crib fires. The etal plate sensor design is shown below in Fig The actual sensor is shown in Fig Throughout this report this sensor will be referred to as the etal plate sensor to differentiate it fro the Gardon type heat flux gauges which are referred to as heat flux gauges. Therocouple spot welded to etal plate Loosely packed Saffil Mat (insulating blanket) Insulating Kaowool 3 board.25 Metal plate Figure 3.2: Metal Plate Sensor Figure 3.3: Built Plate Sensor The sensor construction was straightforward; first a 2 thick steel plate was cut into.25 x.25 pieces. This steel plate was first roughened using a sand blaster and then 33

48 oxidized using a propane torch in order to increase plate eissivity. The eissivity was then further increased by spraying Medther Heat flux gauge paint onto the surface of the plate with a known eissivity of.9. A.76 long piece of.25 x.25 square Kaowool 3 insulating board was then hollowed and filled with Saffil Mat insulating blanket. The blanket was packed loosely to ensure air gaps within the insulation in order to further decrease conduction losses fro the etal plate. A K type therocouple was then spot welded to the back of the etal plate and the plate attached to the board. This etal plate sensor is used adjacent to a Gardon type heat flux gauge and both a gas and a wall teperature therocouple. The copartent setup for these sensors is shown below in Fig The energy balance for the etal plate sensor is: c A dt dt + q& cond 4 fire, r fire, c ( T T ) + ε σt = q& + h (3.8) g In Eq. 3.8 the unsteady ter represents the heating of the etal plate; the therocouple ebedded in the plate easures T. The plate was chosen to be thin to iniize the effects of the transient heating ter. The conductive losses, q & cond, are fro the plate to the board and blanket behind it. On the right hand side of the equation the radiative heat flux fro the fire, & q fire, r, represents both the radiation fro the flaes and the plue. The convective heat transfer coefficient, h,, is taken to be the sae for both convection to the wall and to the etal plate. The conduction loss is deduced though calibration which will be discussed in the next section. The energy balance for the heat flux gauge is: fire c 34

49 HFG 4 ( T T ) ε σt q& = q& + h (3.9) fire, r fire, c g HFG HFG HFG The data collected fro the heat flux gauge easures q & HFG. The heat flux gauge is cooled to roo teperature by cold water being re-circulated behind its face. THFG will be taken to be at abient teperature, T, throughout the rest of this study. Plate Sensor Heat flux fro fire T Heat flux gauge T g Inside Copartent T HFG T w Gas teperature therocouple Copartent Wall Therocouple ebedded in wall Figure 3.4: Plate Sensor, Heat Flux Gauge and Therocouple Setup Vertical View The wall energy balance is: q& 4 cond w w Tw q, + σ = & fire, r + h fire, c ( T T ) ε (3.1) Fro Eq. 3.8, Eq. 3.9 and Eq. 3.1 there are a total of three equations and three unknowns. The easured and unknown quantities are suarized in Table 3.1. g w Table 3.1: Suary of Unknown and Measured Variables Measured Unknown & T g T w T q & HFG q fire, r h fire, c q & cond, w 35

50 Using the above setup the convective and radiative heat transfer coponents fro the fire to the copartent walls can be differentiated and the conduction losses through the wall aterial easured Calibrating Sensor Conduction Loss and Tie Response Sensor calibration was conducted to resolve the conduction loss. Calibration was conducted using a heat flux gauge and etal plate sensor placed incident to the sae radiant heat flux source as shown in Fig The radiant heat flux source in this case is a radiant panel which burns propane. T Heat Flux Gauge T q& inc Plate Sensor L T Radiant Panel Mounting Support Figure 3.5: Sensor Calibration Setup A steady state radiant heat flux fro the panel is reached before the etal plate sensor is placed within its ounting support incident to the panel. The incident heat flux did vary slightly during testing. The energy balance for the plate sensor in the above setup is: c A dt dt 4 4 ( T T ) hc plate ( T T ) q& cond = α (3.11) q& inc σε, 36

51 In Eq. 3.11, q& inc represents the incident radiation heat flux fro the radiant panel and α the absorbtivity of the etal plate. When the teperature of the etal plate sensor reaches steady state, the energy balance, Eq. 3.11, siplifies to: 4 4 ( T T ) + hc plate ( T T ) + q& cond & inc = σε, α q (3.12) The heat flux gauge easures the incident heat flux, q & inc, and etal plate sensor teperature data is recorded. The conduction loss is rewritten using the linear approxiation to Fourier s equation as: ( T T ) ( T ) cond = k = hk T q& (3.13) δ The above assuption is needed to linearize the etal plate sensor and is justifiable since this ter is expected to be sall. The etal plate sensor convective heat transfer coefficient can be calculated by using the theory for free convection fro a vertical plate. The Gr nuber is first calculated to deterine whether the flow is lainar or turbulent. The Gr nuber is defined as [6]: gβ Gr υ 2 ( T T ) L 3 (3.14) The length scale L in Eq is the length of insulating board upon which the heat flux gauge and etal plate sensor are ounted. The ount is of diensions.254 square. If Gr<<1 9 the flows across the plate are lainar, and by setting Pr =.71, Nu can be calculated using [6]: 1/4 3 1/2 Gr Pr Nu = 4 (3.15) 1/2 ( Pr Pr) 1/ 4 37

52 The convective heat transfer coefficient for a steady state etal plate sensor teperature can then be solved for fro the definition of the Nu nuber and a specified conductivity for air, k air : h c, platel Nu = (3.16) k air The effective conduction loss coefficient can be calculated by rearranging the steady state energy balance equation for the plate: h k α q& = inc σε 4 4 ( T T ) h ( T T ) ( T T ) c, plate (3.17) Fig. 3.6 below is a plot of the conductive losses fro the plate sensor as a function of the incident flux. Fig. 3.7 below plots the conductive coefficient calculated fro Eq above for various sensors constructed Conduction Loss (kw/ 2 ) 4 3 s1 2 s2 s3 s4 s5 s6 1 s7 s8 s9 s Incident Flux (kw/ 2 ) Figure 3.6: Conductive Losses fro Metal Plate Sensor as a Function of Incident Flux 38

53 2 x Conductive Coefficient (kw/ 2 K) Steady State Incident Flux (kw/ 2 ) s1 s2 s3 s4 s5 s6 s7 s8 s9 s1 Figure 3.7: Metal Plate Sensor Conductive Heat Loss Coefficient Fro Fig. 3.7 it is seen that for low incident flux the etal plate sensor has a positively sloped linear response to the incident flux which becoes constant at a flux higher than 5 kw/ 2. The correlation for the conductive heat loss coefficient is: h k 3. 1 q& 3 inc = q& inc q& inc kw < 5 2 kw 5 2 (3.18) The legends for Fig. 3.6 to Fig. 3.1 are labeled S1 to S1 in reference to the ten etal plate sensors built for the experients. In order for the data collected fro the etal plate sensor to be eaningful, the tie response of each etal plate sensor needs to be calculated. This tie response can then be used to correct the inherent lag present in the etal plate sensor data. 39

54 The etal plate sensor radiation heat loss ter is first re-expressed as: ( T T ) = σε ( T + T )( T + T )( T T ) σε (3.19) Substituting Eq into the unsteady energy balance, Eq. 3.11, for the plate sensor gives: c A dt dt ( T T ) = α q& h (3.2) inc eff The effective heat transfer coefficient, h eff, represents: h eff 2 2 ( T + T )( T ) = h + h + σε T (3.21) c k + The easured etal plate sensor heat flux is taken to be: 4 4 ( T T ) + h ( T T ) + h ( T T ) = h ( T ) q& = σε T (3.22) c Eq is then substituted into the energy balance, Eq. 3.2 to give: k eff ( c) A h eff dq& dt + q& = α q& (3.23) inc Defining the diensionless tie variable: t τ = (3.24) ( c) A h eff The energy balance, Eq. 3.23, can be rewritten as: dq& dτ = α q& inc q& (3.25) Using the initial condition that the etal plate sensor initially easures zero flux, q& ( ) =, Eq is solved giving: 4

55 h eff A ( ) t c q& = α q& inc 1 e (3.26) Fro the above solution the etal plate sensor tie response is: ( c) t r = (3.27) heff A If the expression for the effective heat transfer coefficient, Eq. 3.21, of the plate is substituted into the Eq above it becoes explicit that there is teperature dependence in the tie response: t r ( c) 2 ( T + T )( T T ) = 2 + [ h c + h k + σε ] A (3.28) Solving the energy equation, Eq. 3.2, in ters of teperature using the initial condition that the etal plate sensor is initially at abient teperature gives the solution below where steady state teperature is T ss : t t T r ss 1 e (3.29) ( T ) = ( T T ) For a particular steady state panel incident radiant flux there will be a unique tie response for a etal plate sensor. When recorded tie, t, equals response tie, t r, Eq reduces to: ( T T ) ( T T ) ss = 1 e 1 (3.3) Therefore fro the recorded teperature data a easured tie response can then be calculated. Fig. 3.8 below plots etal plate sensor tie response as a function of steady state plate teperature and Fig. 3.9 as a function of steady state incident heat flux. 41

56 t r (s) s1 s2 s3 s4 s5 s6 s7 s8 s9 s T ss ( o C ) Figure 3.8: Metal Plate Sensor Tie Response against Steady State Teperature Fig. 3.8 above agrees with the theory fro Eq which indicated that there is teperature dependence in the etal plate sensor tie response. 42

57 t r (s) s1 s2 s3 s4 s5 s6 s7 s8 s9 s Steady State Incident Flux (kw/ 2 ) Figure 3.9: Metal Plate Sensor Tie Response against Incident Flux Having calibrated the etal plate sensor conduction loss and tie response, t r,, the effective ass, heat capacity and plate area can then be solved using the following expression: 2 [ h h + ( T + T )( T + T )] 2 t = ( c) r, c + k σε (3.31) A Metal plate sensor easured, ( c ) A, is plot below in Fig

58 c/a (kj/ 2 K) s1 s2 s3 s4 s5 s6 s7 s8 s9 s Incident Flux (kw/ 2 ) Figure 3.1: Metal Plate Sensor Properties Calibration Results c The easured etal plate sensor properties, A value of approxiately 3.21 kj/kg K., plot in Fig. 3.1 is constant with a 44

59 3.2.2 Corrected Sensor Output Eq is solved nuerically to obtain etal plate sensor data which has been corrected for the sensor tie response. At each tie step the etal plate sensor tie response is coputed using Eq The differential is coputed nuerically using a forward difference schee. Sapling period is used as the tie step. ( t + 1) q& ( t) q& tr + q& () t = q&, α inc () t (3.32) t The value obtained fro nuerically solving the left hand side of Eq above then gives the incident flux fro the radiant panel. Fig and Fig below illustrate exaples of a corrected calibration response in the case of etal plate sensors 1 and 2. In the legends of the figures below Q is the uncorrected etal plate sensor signal, Q crr the signal calculated using Eq above and Q inc the easured incident radiant panel heat flux fro the heat flux gauge. The sensor easured response follows the incident heat flux closely once corrected. This provides a validation of the linear theory used to approxiate the etal plate sensor response. The plate incident flux is seen as an approxiate step function by the plate sensor though it can be noticed that there is a slight increase in incident flux with tie during the calibration. The turn off point during the calibration is viewed by the etal plate sensor as a step change in its input which then results in instabilities in the corrected sensor response. In the actual copartent, the fire will effectively provide a continuous signal seen by the etal plate sensor which can be correct without the discontinuities affecting the response as seen below. 45

60 4 3 Qinc Q Qcrr 2 Heat Flux (kw/ 2 ) Tie (s) Figure 3.11: Sensor Measured and Corrected Response Sensor Qinc Q Qcrr 1 Heat Flux (kw/ 2 ) Tie (s) Figure 3.12: Sensor Measured and Corrected Response Sensor 2 46

61 3.2.3 Sensor Tie Response in Copartent Fires Since the etal plate sensor has been proven to accurately easure a step change incident heat flux it can now be calibrated for use in copartent fires. The etal plate sensor tie response when used in the copartent fire differs fro the calibration case. Taking another look at the energy balance for the etal plate sensor: c A dt dt + q& cond 4 fire, r fire, c ( T T ) + ε σt = q& + h (3.33) g The etal plate sensor incident heat flux is: inc fire = q&, fire, r + h fire, c ( T T ) q& (3.34) g Expanding the radiation and conduction loss ters as done previously in Eq and Eq. 3.19, gives a new effective heat loss coefficient: h 2 2 ( T + T )( T ) eff, fire = hk + σε + T (3.35) The sensor easured heat flux is: 4 4 ( T T ) + ε σ ( T ) q& = h T (3.36) k Substituting Eq into the energy equation balance, Eq. 3.33, and using the diensionless tie, τ, defined in Eq results in the following first order differential equation: dq& + q& dτ = q& inc, fire (3.37) The tie response for the etal plate sensor when used in a copartent fire is: t ( c) r, fire = (3.38) A heff, fire 47

62 4. EXPERIMENT DESIGN AND METHODOLOGY In chapter 4 the ethodology used to design the experients which were then used to investigate the scaling of heat flux within copartent fires is laid out. This process begins with the developent of the copartents at each scale; full scale, 1/8 scale, 1/4 scale and 3/8 scale. The copartent fuel load and wall aterial design are then explained. The locations of the sensors used in obtaining the heat flux data fro the copartent fires are illustrated. Finally a brief discussion is given on the technique used to ignite the wood cribs. 4.1 Design Requireents for Scaling Validation Experients To test the new scaling theory developed in chapter 2 and understand the scaling of heat flux in copartent fires a series of experients were constructed within the fraework outlined below. 1) Wood cribs ust burn in porosity controlled regie. 2) The full scale wood crib ust have a burn tie of one hour. 3) The sallest wood crib ust have a iniu of 5 sticks per layer and 4 layers. 4) Full scale fuel load should represent a realistic occupancy loading. 5) Full scale copartent will be of diensions 3.76 x 3.76 x ) Full scale wall aterial will be Gypsu Board with a thickness of 15.9 The porosity requireent is satisfied by setting the iniu crib porosity at.7. Fro Fig. 2.6 it was seen that the iniu porosity to be in such a burn regie is.5. A porosity of.7 was chosen to include a argin of error into the design. A 48

63 larger porosity was not chosen as crib size and its associated costs, increases proportionally with porosity. The one hour burn tie requireent was specified with the future goal of placing a structure within the copartents to test structural fire scaling. A one hour burn tie will then replicate a standard fire resistance test for a building assebly [3]. The third requireent denotes a iniu crib size, below which the crib scaling theory does not hold, [3]. The final three requireents of the fraework were based upon the desire to build a realistic copartent [3]. Three scale odels, 1/8, 1/4 and 3/8, of the full scale copartent were then designed to fit the space constraints of the current laboratory facilities Full Scale Crib and Vent Design In creating a design fire of one hour using wood cribs taking factors such as expense and facility space into account it becae apparent that a free burning copartent fire was ipracticable. A one hour free burning copartent fire would also require a wood crib whose area would exceed the floor area of the copartent. It was therefore decided to design a ventilation liited fire. Harathy [14] studied the burning rate of wood cribs in copartents under different ventilation conditions. Fig. 4.1 below illustrates his results. The relationship for burning rate and air flow rate into the copartent was derived for ventilation liited conditions to be [14]: & =. 163 (4.1a) U f U a 1/ 2 1/ 2 a =.145ρ g Ao h (4.1b) 49

64 In Eq. 4.1, U a is the flow rate of air through the vent, A o is the vent area and h, the vent height. For siplicity the vent height was fixed to the full scale copartent height and only its width varied. Figure 4.1: Burning Rate Behaviour of Cribs in Copartents [14] In developing the full scale crib the requireent for the sallest scale, in this case the 1/8 scale, to have 5 sticks per layer and 4 layers results in the full scale crib having 28 sticks per layer and 8 layers, by the wood crib scaling laws in Table 2.5. Both paraeters have been rounded to the nearest whole nuber since partial sticks and layers are not possible. The reaining wood crib design variables are stick length and thickness. The surface area of a crib, without overlap was derived to be: 5

65 2 d A s = nb 1 n + 2 2N + 2n b d b (4.2) Substituting Eq. 4.2, Eq and Eq into Eq. 2.7: P = A A v s s 1/ 2 b 1/ 2 = nb 2 ( d nb) 5 / 2 ( n 1) 1 n + 2 d b 1/ 2 b 1/ 2 d 2N + 2n b (4.3) By setting porosity to.7 the above result can be re-arranged to give: 2 d d ( ) 5 / nb n + N + n d nb ( n 1) 1/ b 1/ = (4.4) b b Given a fixed stick thickness, the iniu stick length was calculated to satisfy Eq. 4.4 using a siple optiization algorith. Once the crib paraeters for a full scale crib are set and its ass calculated, the burn tie is coputed using Eq. 4.1a and Eq. 4.1b. The copartent vent size can then be varied until a burn tie of approxiately 7 inutes is reached. Finally loading on the copartent floor is calculated and copared against a standard office occupancy loading of 12 pounds per square foot (psf), or Pa [15]. This process was repeated until a satisfactory burn tie and loading was reached. Fig. 4.2 below shows a plot of varying vent size and burn tie for various full scale crib stick thickness. 51

66 b=.51 b=.48 b=.45 b=.42 b=.39 Burn Tie (inutes) Vent Width () Figure 4.2: Burn Tie for Different Stick Thicknesses A burn tie of 7 inutes at full scale was chosen to include a argin of error in the design. In the final design a full scale thickness of.45 was chosen with a full scale copartent vent width of.5. The full scale loading was psf or Pa. Table 4.1 below suarizes the crib design at each scale. Rounding error fro the nuber of sticks per layer and layers calculation results in changes in the porosity fro the design value of.7. Table 4.1: Final Large Crib Design Paraeters Scale b () d () n N Porosity () / / /

67 The sall crib design was based on a burn size that would be approxiately 1/1th that of the large fire. Table 4.2 below outlines the specifications for the sall crib design. Table 4.2: Sall Large Crib Design Paraeters Scale b () d () n N Porosity () / / / Copartent Wall Material Design The copartent wall aterial design involved selecting appropriate insulating aterials with properties that atched Gypsu board at full scale. This eant calculating both the π 3 and π 4 groups for a specific aterial thought to be appropriate at a specific scale and coparing it against the π 3 and π 4 groups for gypsu board. For exaple, an appropriate 1/8 scale aterial would be an insulating blanket. Using data for these blankets provided by Kaowool the π 3 and π 4 groups could be calculated and the aterials copared to gypsu board. The aterials with the closest atch to gypsu board at each scale were then selected. Fig. 4.3 and Fig. 4.4 below illustrate the ability of the selected copartent wall aterials to atch that of gypsu board at full scale. 53

68 k ρ c ( 2 /s) Gypsu Board Saffill Mat Kaowool 3 Kaowool S Teperature ( o C ) Figure 4.3: Scaled Wall Material Properties Plot against Gypsu Board Copartent wall aterials chosen cae with a specified anufacturer thickness. Using these thickness and the aterial properties the π 4 group for each of the aterials was plot against teperature, Fig

69 12 1 Saffil Mat Kaowool 3 Kaowool S 8 π Teperature ( o C ) Figure 4.4: Materials Scaled π 4 Group Copared to Gypsu Board The three aterials which were the closest atched to gypsu board were Saffil Mat, Kaowool 3 Board and Kaowool S board for the 1/8, 1/4 and 3/8 scale copartents respectively. Their thicknesses at their respective scales were 34 for the Saffil Mat and 13 for the two boards. 55

70 4.1.3 Proposed Testing Schedule An experient atrix was then developed for the copartent fires. Due to the size of the 3/8 scale copartent and lack of available facilities to conduct experients of this size, it was only possible for 1/8 and 1/4 scale copartent fires to be conducted. Two sall and large fires were conducted at the 1/8 scale and one of each was conducted at the 1/4 scale. Table 4.3 below suarizes the test schedule and the acronys for each test. Table 4.3: Copartent Burn Testing Schedule Test ID Description 1/8SF1 1/8 Scale sall fire Burn 1 1/8SF2 1/8 Scale sall fire Burn 2 1/8LF1 1/8 Scale large fire Burn 1 1/8LF2 1/8 Scale large fire Burn 2 1/4SF1 1/4 Scale sall fire Burn1 1/4LF2 1/4 Scale large fire Burn1 56

71 4.2 Copartents and Sensor Setup The full scale copartent of diensions 3.76 x 3.76 x 2.54 corresponding to its width, length and height respectfully, has to be scaled geoetrically to design three copartents at 1/8, 1/4 and 3/8 scales. These copartents have diensions listed below in Table 4.4. Table 4.4: Suary of Copartent Diensions Copartent Scale Diensions () (W x L x H) 1/8.47 x.47 x.32 1/4.94 x.94 x.635 3/ x 1.41 x.95 Four sensor locations were selected for the 1/8 scale copartent. These were on the upper left and right walls, the ceiling and the lower back wall. The first three locations were used to gather heat flux data in the upper layer of the fire in the copartent and the forth location was in the lower layer of the fire. Fig. 4.5, Fig. 4.6 and Fig. 4.7 illustrate the location of the sensors in the 1/8 scale copartent. 57

72 Figure 4.5: 1/8 Scale Copartent Sensor Setup The Fig. 4.5 shows the sensor setup with the copartent floor and vents cut away. Fig. 4.6 below shows the setup fro the outside looking at the copartent fro the rear. Figure 4.6: 1/8 Scale Copartent Sensor Setup - Rear View Diensions 58

73 Figure 4.7: 1/8 Scale Copartent Sensor Setup - Top View Diensions Between scales the locations of the sensors are scaled geoetrically to be at hoologous locations. After testing was copleted with the 1/8 scale copartent one of the Gardon type heat flux gauges failed resulting in only three sensor locations being utilized in the 1/4 scale. The sensors were located at the left wall, back wall and ceiling locations hoologous to the sensor locations in the 1/8 scale copartent. Fig. 4.8, Fig. 4.9 and Fig. 4.1 below illustrate the location of the sensors in the 1/4 scale copartent. 59

74 Figure 4.8: 1/4 Scale Copartent Sensor Setup - Front View Figure 4.9: 1/4 Scale Sensor Setup - Diensions 6

75 Figure 4.1: 1/4 Scale Sensor Setup - Diensions 61

76 Sensor locations are labeled using a coordinate syste based on their position relative to the height, H, width, W, or depth, D, of the copartent. Since the sensor locations were hoologous between scales, these positions are identical in both the 1/4 and 1/8 scale copartents. The origin (,,), is located at the back wall lower left hand corner of the copartent. The front wall, right upper corner is the (D,W,H) coordinate. Fig below illustrates this labeling convention. Table 4.5 below lists the coordinate locations of the sensors in the copartents. The location chosen to represent the sensor setup was the plate sensor location. H D W Figure 4.11: Coordinate Labelling Convention Table 4.5: Sensor Setup Coordinates Sensor Location Coordinate Left Wall (.44D,,.65H) Back Wall (,.55W,.2H) Ceiling (.44D,.37W,H) Right Wall (.55D,W,.65H) 62

77 Plate Sensor Heat Flux Gauge Figure 4.12: Sensor Setup - 1/8 Scale Copartent Figure 4.13: Left Wall, Ceiling and Back Wall Sensor Setup - 1/8 Scale Copartent 63

78 Plate Sensor Wall and Gas Therocouples Heat Flux Gauge Figure 4.14: Sensor Setup - 1/4 Scale Copartent Figure 4.15: Left and Ceiling Sensor Setup - 1/4 Scale Copartent 64

79 4.2.1 Ignition of Wood Cribs Wood cribs were placed in an oven at 15 o C for 48 hours prior to each burn to ensure that its oisture content was as low as possible. The cribs were ignited using a heptane pool fire. This pool fire was scaled between copartents and fuel loads. For each crib a square pan was constructed which was 125% larger than the base area of the crib and 2 in depth. It was decided that a.5 deep heptane pool would be used for each crib as its ignition source [3]. The crib was then elevated above the lip of the fuel pan at a distance equal to the particular crib s stick thickness. Fig below illustrates a scheatic of the wood crib, pan and crib elevator prior to a burn. Pan Crib Elevator Figure 4.16: Wood Crib and Pan Pre-Burn Setup 65

80 5. RESULTS This chapter presents and discusses results fro the experients designed in chapter 4. In the first part of this chapter, prior results are presented fro work conducted by Perricone [3] to deonstrate the overall viability of new scaling theory. Following this results are shown to illustrate the repeatability of wood crib fires. Sensor data is then presented to illustrate the effectiveness of the novel etal plate sensor to differentiate between the convective and radiative heat fluxes in copartent fires. Scaling results are then presented and finally a correlation for the convective heat transfer coefficient data is derived based upon teperature rise within the copartent. 5.1 Prior Scaling Results and Data Coparisons Before analyzing data fro the experients conducted in this thesis a brief outline of scaling results fro Perricone [3] are presented. Perricone s data presents a strong arguent in favor of the current scaling approach. These results then initiated further research into the scaling ethodology which then becae the basis for this thesis and ongoing work on scaling structures in fires. Where possible, data fro tests conducted in both studies is copared to ephasize the repeatability of the wood crib fire data. 66

81 5.1.1 Free Burn Results Before conducting copartent fire experients a series of free burn experients were conducted using the wood cribs designed for each scale. During these experients the 3/8 scale was also tested as laboratory facilities provided by the ATF b were available. Both the sall crib and large crib designs were evaluated. The experiental labeling convection adopted by Perricone [3] is outline in Table 5.1. Table 5.1: Perricone Test Identification Test Description 1-L-C/F-1/2 1/8 Scale Large fire 2-L-C/F-1/2 2/8 Scale Large fire 3-L-C/F-1/2 3/8 Scale Large fire 1-S-C/F-1/2 1/8 Scale Sall fire 2-S-C/F-1/2 2/8 Scale Sall fire 3-S-C/F-1/2 3/8 Scale Sall fire The nuerical suffix in the test labels in Table 5.1 are used to differentiate between repeated experients. In the case where the fire is a free burn, the letter F is used instead of C which indicates a copartent burn. Fig. 5.1 and Fig. 5.2 below plot the scaled crib free burning rate data, π 2, for the large and sall fires respectively. The π 2 group has been plot against the diensionless tie, τ: 1/ 2 g τ = t (5.1) l b Bureau of Alcohol, Tobacco and Firears 67

82 Figure 5.1: Diensionless Free Burning Rate Results - Large Crib Design [3] Figure 5.2: Diensionless Free Burning Rate Results - Sall Crib Design [3] Fig. 5.1 and Fig. 5.2 show the ability of the current scaling ethodology to scale the burning rate of free burning wood cribs. The free burning rates for both the sall and large wood cribs have been successfully scaled between the 1/8, 1/4 and 3/8 scales. 68

83 These results also indicate that the ethodology used in scaling the wood crib paraeters was successful Copartent Burning Rate Data Fig. 5.3 below plots the scaled burning rate for the large wood cribs in the copartents. As with the free burn data the π 2 group at each scale has been plot against the diensionless tie, τ. Figure 5.3: Diensionless Copartent Burning Rate Results - Large Crib Design [3] Fro Fig. 5.3 it is concluded that the transient burning rate behavior of the wood cribs in copartents has been scaled. There is soe variation in the scaled burning rate behavior between the three scales which is due to the uneven ignition characteristics of the cribs. 69