Bench Scale Apparatus Measurement Uncertainty and Uncertainty Effects on Measurement of Fire Characteristics of Material Systems by Lei Zhao A Thesis Submitted to the Faculty of the WORCESTER POLYTECHNIC INSTITUTE In partial fulfillment of the requirements for the Degree of Master of Science In Fire Protection Engineering By May 2005 APPROVED: Professor Nicholas A. Dembsey, Major Advisor Dr. John L. de Ris, Co-Advisor FM Global Research Dr. Robert Bill, Co-Advisor FM Global Research Professor Kathy A. Notarianni, Head of Department ABSTRACT Traditional probability and statistics methodologies recommended by ISO and NIST were applied to standardize measurement uncertainty analysis on calorimetry bench scale apparatuses. The analysis was conducted for each component instrument (direct measurement) and each related physics quantity measured indirectly. There were many sources contributing to the ultimate uncertainty, however, initially, we dealt with the intrinsic uncertainty of each measuring instrument and the uncertainty from calibration. All other sources of uncertainty, i.e., drift, data acquisition, data reduction (round off, truncation, and curve smoothing) and personal operation were assumed to be negligible. Results were expressed as an interval having 95% confidence that the “true” value would fall within. A Monte Carlo Simulation technique with sampling size of 10000 was conducted to model the experiments. It showed that at least 95% of the modeled experiment results were inside the estimate interval. The consistency validated our analysis method. An important characteristic of composite material systems is the ability to “custom design” the system to meet performance criteria such as cost, durability, strength and / or reaction to fire. To determine whether a new system is an improvement over previous ones and can meet required performance criteria, sufficiently accurate and precise instruments are needed to measure the system’s material properties in bench scale testing. Commonly used bench scale apparatuses are the cone calorimeter (Cone) and the FMGR fire propagation apparatus (FPA). For this thesis, thermally “thin” and “thick” specimens of a natural composite, red oak, were tested in the Cone in an air environment and in the FPA in a nitrogen environment. Cone test data of two FRP composite systems from the previous work of Alston are also considered. The material reaction to fire properties were estimated considering both ignition and i pyrolysis measurements made via the Cone and FPA. Investigation of the ultimate uncertainty of these material fire properties based on the intrinsic uncertainty of the component instruments (e.g. load cell) as well as the uncertainty introduced via use of a current ignition and pyrolysis model are considered. ii ACKNOWLEDGEMENTS I am deeply indebted to my advisor Professor Nicholas A. Dembsey for a lot more than his help, encouragement, and advice, and for a lot more than skills and knowledge that I learned from him. His words of wisdom, insight, and philosophy are among the best things that I have learned. I would also like to thank Dr. John L. de Ris and Dr. Robert Bill for enthusiasm and guidance. Their time and sharing their knowledge and invaluable insight is greatly appreciated. I am highly appreciative of FM Global Research for providing me continuous and generous financial support. The thesis would not have been possible without the support. I couldn’t have done the thesis without the love and support of my wife and my parents. Especially, my wife has always been there to pick me up during the low points as well as to celebrate the good days. My sanity is indebted to her. iii TABLE OF CONTENTS ABSTRACT ...................................................................................................................i ACKNOWLEDGEMENTS...............................................................................................iii LIST OF FIGURES..........................................................................................................vii LIST OF TABLES..............................................................................................................x NOMENCLATURE...........................................................................................................xi DOCUMENT ORGANIZATION AND THESIS OVERVIEW.......................................1 DOCUMENT ORGANIZATION -- GUIDE TO APPENDICES..................................1 THESIS OVERVIEW.....................................................................................................5 CONCLUSIONS...........................................................................................................11 REFERENCES..............................................................................................................13 APPENDIX A MEASUREMENT UNCERTAINTY ANALYSIS FOR CALORIMETRY APPARATUSES...............................................................................A-1 ABSTRACT................................................................................................................A-1 INTRODUCTION.......................................................................................................A-2 BACKGROUND.........................................................................................................A-4 UNCERTAINTY ANALYSIS OF COMPONENT INSTRUMENT (DIRECT MEASUREMENT).....................................................................................................A-6 1. Load Cell..............................................................................................................A-6 2. Laser..................................................................................................................A-15 3. Oxygen Analyzer...............................................................................................A-25 4. Pressure Transducer.........................................................................................A-30 5. Thermocouple....................................................................................................A-31 6. CO/CO Analyzer..............................................................................................A-31 2 UNCERTAINTY ANALYSIS OF INDIRECT MEASUREMENT........................A-32 1. Heat Release Rate..............................................................................................A-34 2. Extinction Coefficient........................................................................................A-49 3. Average Specific Extinction Area.....................................................................A-51 4. Average Heat of Combustion............................................................................A-54 UNCERTAINTY ANALYSIS METHODS VALIDATION BY MONTE CARLO SIMULATION (MCS)..............................................................................................A-56 MANUFACTURER VALUE VS. CURRENT ANALYSIS....................................A-59 CONCLUSIONS.......................................................................................................A-62 REFERENCES..........................................................................................................A-64 APPENDIX B UNCERTAINTY EFFECTS ON MEASUREMENT OF FIRE CHARACTERISTICS OF MATERIAL SYSTEMS.....................................................B-1 ABSTRACT................................................................................................................B-1 INTRODUCTION.......................................................................................................B-1 BACKGROUND.........................................................................................................B-3 PYROLYSIS MODEL................................................................................................B-3 SPECIMEN PREPARATION....................................................................................B-5 TEST SETUP..............................................................................................................B-6 PROPERTY ESTIMATION......................................................................................B-7 1. ESTIMATION OF BASELINE PROPERTIES....................................................B-8 1.1 Red Oak Tested in Air Environment Using Cone............................................B-8 1.2 Red Oak Tested in Nitrogen Environment Using FPA...................................B-11 1.3 Composites Tested in Air Environment Using Cone.......................................B-14 2. PROPERTY ESTIMATION WITH MLR UNCERTAINTY..............................B-16 2.1 MLR and Its Uncertainty Calculation.............................................................B-17 iv 2.1.1 MLR Calculation.......................................................................................B-17 2.1.2 Uncertainty of MLR Calculation..............................................................B-17 2.2 Property Estimation with One Standard Deviation of MLR..........................B-19 2.2.1 Red Oak Tested in Air Environment Using Cone and in Nitrogen Environment Using FPA....................................................................................B-19 2.2.2 Composites Tested in Air Environment Using Cone................................B-20 CONCLUSIONS........................................................................................................B-21 ACKNOWLEDGEMENTS.......................................................................................B-22 REFERENCES...........................................................................................................B-22 APPENDIX C DERIVATION OF WELCH-SATTERTHWAITE FORMULA1,2....C-1 1. RELATIONSHIP BETWEEN DISTRIBUTIONS................................................C-1 1-1 Normal and Standard Normal Distribution.....................................................C-1 1-2 Standard Normal and Chi Squared Distribution.............................................C-1 1-3 Summation of Chi Squared Distribution.........................................................C-2 1-4 Standard Normal, Chi Squared and Student’s t Distribution.........................C-2 2. W-S FORMULA DERIVATION...........................................................................C-3 REFERENCES............................................................................................................C-5 APPENDIX D C-FACTOR DETERMINATION1......................................................D-1 REFERENCE..............................................................................................................D-4 APPENDIX E LASER PHOTODIODES POWER CYCLE INVESTIGATION......E-1 APPENDIX F A HYPOTHETICAL CALIBRATION FOR OXYGEN ANALYZER... ..........................................................................................................F-1 REFERENCES.............................................................................................................F-4 APPENDIX G STANDARD DEVIATION OF UNIFORM DISTRIBUTION1.........G-1 REFERENCE..............................................................................................................G-2 APPENDIX H CONE VIs INTRODUCTION.............................................................H-1 APPENDIX I LOAD CELL SYSTEM AND LASER SYSTEM RESPONSE TIMEI-1 APPENDIX J JUSTIFICATION OF UNCERTAINTY PROPAGATION EQUATION1 ...............................................................................................................J-1 REFERENCE...............................................................................................................J-4 Appendix K HRR UNCERTAINTY BASED ON METHANE...............................K-1 REFERENCES............................................................................................................K-2 APPENDIX L BACKGROUND OF UNCERTAINTY ANALYSIS RELATED TO RECOMMENDED METHODOLOGIES.....................................................................L-1 REFERENCES............................................................................................................L-3 APPENDIX M MEASUREMENT ERROR AND UNCERTAINTY.........................M-1 REFERENCES...........................................................................................................M-2 APPENDIX N MASS LOSS RATE UNCERTAINTY................................................N-1 REFERENCES............................................................................................................N-2 APPENDIX O SENSITIVITY ANALYSIS FOR HRR...............................................O-1 REFERENCE..............................................................................................................O-3 APPENDIX P VOLUME FLOW RATE.....................................................................P-1 REFERENCES.............................................................................................................P-4 APPENDIX Q SENSITIVITY ANALYSIS FOR EXTINCTION COEFFICIENT...Q-1 REFERENCE..............................................................................................................Q-2 APPENDIX R SMOKE PRODUCTION RATE.........................................................R-1 REFERENCES............................................................................................................R-5 APPENDIX S DYNAMIC SPECIFIC EXTINCTION AREA....................................S-1 REFERENCES.............................................................................................................S-6 APPENDIX T DYNAMIC HEAT OF COMBUSTION.............................................T-1 v REFERENCES............................................................................................................T-3 APPENDIX U CONSTANT MLR GENERATOR FOR FUTURE WORK..............U-1 vi LIST OF FIGURES Figure A-1 Load Cell Residual Dispersion.....................................................................A-9 Figure A-2 Load Cell Measured Values vs. Accepted Values of Reference MaterialsA-10 Figure A-3 Schematic Diagram of a Control Chart for Load Cell..............................A-14 Figure A-4 Laser Main Photodiode Normalized Residual Dispersion........................A-18 Figure A-5 Laser Compensation Photodiodes Normalized Residual Dispersion.......A-19 Figure A-6 Measured Values vs. Accepted Values of Reference Materials for Main Photodiode.............................................................................................................A-19 Figure A-7 Measured Values vs. Accepted Values of Reference Materials for Compensation Photodiode....................................................................................A-20 Figure A-8 Schematic Diagram of a Control Chart for Laser Main Photodiode.......A-23 Figure A-9 Schematic Diagram of a Control Chart for Laser Compensation Photodiode ................................................................................................................................A-24 Figure A-10 Manufacturer’s Uncertainty and Current Uncertainty Comparison for Oxygen Analyzer...................................................................................................A-30 Figure A-11 Heat Release Rate and Its 95% Confidence Interval for 38mm Red Oak at 40 kW/m2 External Heat Flux in Cone Test.........................................................A-36 Figure A-12 Heat Release Rate and Its 95% Confidence Interval of 2mm Red Oak at 40 kW/m2 External Heat Flux in Cone Test..............................................................A-37 Figure A-13 Normalized HRR for Ten Days and Its 95% Confidence Uncertainty Band Based on Day-to-Day Variation and 95% Confidence Uncertainty Band based on Calibration for 1 kW Methane Burning Test.......................................................A-44 Figure A-14 Normalized HRR for Ten Days and Its 95% Confidence Uncertainty Band Based on Day-to-Day Variation and 95% Confidence Uncertainty Band based on Calibration for 3 kW Methane Burning Test.......................................................A-45 Figure A-15 Normalized HRR for Ten Days and Its 95% Confidence Uncertainty Band Based on Day-to-Day Variation and 95% Confidence Uncertainty Band based on Calibration for 5 kW Methane Burning Test.......................................................A-45 Figure A-16 HRR Uncertainty and the Normalized HRR Uncertainty (above 100%) of 2mm Red Oak at 70 kW/m2 External Heat Flux in Cone Test............................A-46 Figure A-17 HRR Uncertainty and the Normalized HRR Uncertainty (below 100%) of 2mm Red Oak at 70 kW/m2 External Heat Flux in Cone Test............................A-47 Figure A-18 R Values of the Component Variables for Heat Release Rate Calculation for 2mm Red Oak at 70 kW/m2 External Heat Flux in Cone Test......................A-48 Figure A-19Extinction Coefficient and Its 95% Confidence Interval of 38mm Red Oak at 40 kW/m2 External Heat Flux in Cone Test.....................................................A-50 Figure A-20 R Values of the Component Variables for Extinction Coefficient Calculation for 38mm Red Oak at 40 kW/m2 External Heat Flux in Cone Test A-51 Figure A-21 HRR Uncertainty Comparison Between Current Analysis and Manufacturer’s Value for 38mm Red Oak at 40 kW/m2 External Heat Flux in Cone Test...............................................................................................................A-60 Figure A-22 HRR Uncertainty Comparison Between Current Analysis and Manufacturer’s Value for 38mm Red Oak at 40 kW/m2 External Heat Flux in Cone Test...............................................................................................................A-60 Figure A-23 Normalized HRR Comparison at Different HRR Levels among Current Analysis, Enright et al12, Manufacturer Values (of Cone in WPI), and NIST13.A-62 Figure B-1 Measured and Calculated MLR Comparison for Thermally “Thick” Red Oak at 60 kW/m2 External Heat Flux in Air Using Cone......................................B-9 vii Figure B-2 Measured and Calculated MLR Comparison for Thermally “Thin” Red Oak at 20 kW/m2 External Heat Flux in Air Using Cone.............................................B-10 Figure B-3 Measured and Calculated MLR Comparison for Thermally “Thick” Red Oak at 50 kW/m2 External Heat Flux in nitrogen Using FPA..............................B-12 Figure B-4 Measured and Calculated MLR Comparison for Thermally “Thin” Red Oak at 25 kW/m2 External Heat Flux in nitrogen Using FPA......................................B-13 Figure B-5 Measured and Calculated MLR Comparison for Thermally “Thick” Composite at 50 kW/m2 External Heat Flux in Air Using Cone..........................B-15 Figure B-6 Measured and Calculated MLR Comparison for Thermally “Thin” Composite at 50 kW/m2 External Heat Flux in Air Using Cone..........................B-15 Figure B-7 MLR and Its Uncertainty Bands for Thermally “Thick” Composite at 50 kW/m2 External Heat Flux in Air Using Cone Calorimeter.................................B-18 Figure D-1 Illustration of the Vertical Part of the Exhaust Duct of Cone Calorimeter with Orifice Plate and Pressure Ports....................................................................D-1 Figure E-1 Power Cycle Illustration of Main Photodiode at 16% Reference Obscuration ..................................................................................................................................E-2 Figure E-2 Power Cycle Illustration of Compensation Photodiode at 16% Reference Obscuration.............................................................................................................E-2 Figure E-3 Power Cycle Illustration of Main Photodiode at 100% Reference Obscuration.............................................................................................................E-3 Figure E-4 Power Cycle Illustration of Compensation Photodiode at 100% Reference Obscuration.............................................................................................................E-3 Figure E-5 Output Voltage Standard Deviation of Main Photodiode at Different Reference Obscuration Level..................................................................................E-6 Figure E-6 Output Voltage Standard Deviation of Compensation Photodiode at Different Reference Obscuration Level..................................................................E-6 Figure I-1 Main and Compensation Photodiodes Response Time shown by Changing from 100% Obscuration to 0% Obscuration...........................................................I-1 Figure I-2 Main and Compensation Photodiodes Response Time shown by Changing from 0% Obscuration to 100% Obscuration...........................................................I-2 Figure I-3 Load Cell System Response Time by Weight dropped on the Load Cell......I-3 Figure I-4 Load Cell System Response Time by Weight Taken Away from the Load Cell ....................................................................................................................................I-3 Figure M-1 Illustration of Systematic Error, Random Error and Total Measurement Error (The Figure is Modified from Figure 4.1 of Test Uncertainty2 )................M-1 Figure N-1 MLR and Its 95% Confidence Interval of 2mm Red Oak at 70 kW/m2 External Heat Flux in Cone Test............................................................................N-2 Figure P-1 Five-point Average of Volume Flow Rate and Its 95% Confidence of Interval for 38mm Red Oak at 40 kW/m2 External Heat Flux in Cone Test.......................P-2 Figure P-2 R Values of the Component Variables of Volume Flow Rate Calculation for 38mm Red Oak at 40 kW/m2 External Heat Flux in Cone Test.............................P-3 Figure R-1 Smoke Production Rate and Its 95% Confidence Interval for 38mm Red Oak at 40 kW/m2 External Heat Flux in Cone Test...............................................R-3 Figure R-2 R Values of the Component Variables of Smoke Production Rate Calculation for 38mm Red Oak at 40 kW/m2 External Heat Flux in Cone Test..R-5 Figure S-1Five-Point Average of Dynamic Specific Extinction Area and Its 95% Confidence Interval of 38mm Red Oak at 40 kW/m2 External Heat Flux in Cone Test...........................................................................................................................S-2 viii Figure S-2 R Values of C Factor, Pressure, and Temperature for Dynamic Specific Extinction Area Calculation for 38mm Red Oak at 40 kW/m2 External Heat Flux in Cone Test..............................................................................................................S-4 Figure S-3 R Value of Mass Loss Rate for Dynamic Specific Extinction Area Calculation of 38mm Red Oak at 40 kW/m2 External Heat Flux in Cone Test.....S-5 Figure S-4 R Values of Main and Compensation Photodiodes for Dynamic Specific Extinction Area Calculation of 38mm Red Oak at 40 kW/m2 External Heat Flux in Cone Test..................................................................................................................S-5 Figure T-1 Five-Point Average of R Values of Component Variables for Dynamic HOC Calculation for 38mm Red Oak at 40 kW/m2 External Heat Flux in Cone Test..T-2 Figure T-2 R Values of Component Variables for Dynamic HOC Calculation for 38mm Red Oak at 40 kW/m2 External Heat Flux in Cone Test.......................................T-3 Figure U-1 Constant Mass Loss Rate Generator for MLR Uncertainty Estimate.......U-1 ix