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Numerical Technique for Calculation of Radiant Energy Flux to Targets from Flames

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Numerical Technique for Calculation of Radiant Energy Flux to Targets from Flames iiii«jiiiin«iitfftaw « ^»gJ>^ j rü t 5wr!TKg t‘‘3v>g>!eaBggMglMgW8ro?ftanW This dissertation has been microfilmed exactly as received 66-1874 I SHAHROKHI, Firouz, 1938- NUMERICAL TECHNIQUE FOR CALCULATION OF RADIANT ENERGY FLUX TO TARGETS FROM FLAMES. The University of Oklahoma, Ph.D., 1966 Engineering, mechanical University Microfilms, Inc., Ann Arbor, Michigan j THE UNIVERSITY OF OKLAHOMA GRADUATE COLLEGE NUMERICAL TECHNIQUE FOR CALCULATION OF RADIANT ENERGY FLUX TO TARGETS FROM FLAMES A DISSERTATION SUBMITTED TO THE GRADUATE FACULTY in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY BY FIROUZ SHAHROKHI Norman, Oklahoma 1965 NUMERICAL TECHNIQUE FOR CALCULATION OF RADIANT ENERGY FLUX TO TARGETS FROM FLAMES DISSERTATION COMMITTEE ABSTRACT This is a study to predict total flux at a given surface from a flame which has a specified shape and. dimen­ sion. The solution to the transport equation for an absorbing and emitting media has been calculated based on a thermody­ namic equilibrium and non-equilibrium flame. In the thermodynamic equilibrium case, it is assumed that the cir­ cumstances are such that at each point in the flame a local temperature T is defined and the volume emission coefficient at that point is given in terms of volume absorption coeffi­ cient by the Kirchhoff's Law. The flame's monochromatic intensity of volume emission in a thermodynamic equilibrium is assumed to be the product of monochromatic volume extinction coefficient and the black body intensity. In the non-equilibrium case, a measured monochromatic intensity of volume emission of a given flame is used as well as the measured monochromatic volume extinction coefficient. Geometrical relations are derived for sheet, cylinr- drical and conical flames applicable to both thermodynamic equilibrium and non-equilibrium case. The monochromatic flux of a methanol and an acetone flame with a specified shape and dimension to a given target has been calculated and plotted based on these geometrical relations and the iii two methods indicated above. The Gauss numerical integra­ tion method is used to .calculate total radiative flux from the monochromatic flux plots. Some experimental measure­ ments of total radiative flux have been made and compared to the predicted values. IV ACKNOWLEDGEMENT The author wishes to express his deep appreciation to Dr. T.J. Love, Jr. for his guidance and cooperation throughout the progress of this study. The other members of the Doctoral Committee who gave their time and advice also have the author's appreciation and thanks, especially Dr. Omer Pipkin. The author extends his thanks to the staff of the Osage Computer Center. Mr. Paul Johnson's aid in the development of the computer program is sincerely appreciated. Many individuals have made significant contri­ butions to the completion of this study. Most particularly is Mr. James Hood for his active participation and assistance in the experimental phase of the study. The author extends thanks to Mrs. Robert Brown for providing valuable help in preparing this manuscript along with the staff of the Oklahoma University Research Institute; particularly Mr. George Droescher, the draftsman and Mr. Harold Brummer, the reproduction supervisor. Support for this research was provided by Chemical Research and Development Laboratories, Edgewood Arsenal, through Contract DA-18-03 5-AMC-116(A). V Finally, I wish to thank my family for their limitless patience and understanding during the under­ taking and completion of this study ; especially my wife, Kay, who edited and prepared this manuscript; and to my parents, who made it all possible. VI TABLE OP CONTENTS Page LIST OF TABLES........................................ ix LIST OF ILLUSTRATIONS.................................. X Chapter I. INTRODUCTION ................................... 1 Mathematical Presentation of the Problem Previous Theoretical Work II. THEORETICAL BASIS............................... 6 Description of the Methods Used for Monochromatic Flux Prediction III.u GEOMETRICAL EQUATIONS TO CALCULATE MONOCHRO­ MATIC F L U X ................................ 24 Description and Derivation of Geometrical Equations for Sheet, Cylindrical and Coni­ cal Flames IV. NUMERICAL INTEGRATION TO OBTAIN TOTAL FLUX . 39 Gauss Quadrature Method V. CLOSED FORM INTEGRATION...................... 48 Calculation of Total Flux Based on Closed Form Integration VI. EXPERIMENTAL FLUX MEASUREMENTS.............. 54 Description of Apparatus Used for Total Flux Measurement VII. DISCUSSION OF RESULTS........................ 57 VIII. CONCLUSION .................................. 60 vii Chapter Page NOMENCLATURE .......................................... 62 BIBLIOGRAPHY............................................. 65 APPENDICES A. MONOCHROMATIC RADIATION PROPERTIES OF AN ACETONE AND A METHANOLFLAME ................... 72 B. SOME THEORETICAL MONOCHROMATIC RADIATION FLUX CALCULATIONS (METHODS I AND II) OF AN ACETONE AND A METHANOL FLAME WITH A GIVEN SIZE AND POSITION TO A TARGET .......... 103 C. TOTAL RADIATION FLUX CALCULATIONS (METHODS I AND II) AND EXPERIMENTAL RADIATION FLUX MEASUREMENTS OF AN ACETONE AND A METHANOL FLAME WITH A GIVEN SIZE AND POSITION TO A TARGET......................... 178 vxix LIST OF TABLES Table Page I . Monochromatic Radiation Properties of a Methanol Flame Based on Thermodynamic EquJ-librium (41, 44) .............. 73 II. Spectroscopic Radiation Properties of a Methanol Flame (26)........................ 81 III. Monochromatic Radiation Properties of a Methanol Flame (26) .... .............. 85 IV. Spectroscopic Radiation Properties of an Acetone Flame (26) ........................ 92 V. Monochromatic Radiation Properties of an Acetone Flame (26) ........................ 96 IX LIST OF ILLUSTRATIONS Figure Page 1. Geometry for Sheet Flame and Target ...... 28 2. Sheet Flame Side V i e w ..................... 29 3. Geometry for Tilted Sheet Flame .............. 32 4. Geometry for Cylindrical Flame............. 33 5. Geometry for Conical Flame (Target position and angles involved are as shown in Figure 4) . 37 6. Instrumentation........................... 56 7. Spectral Absorptivity of Methanol Flame Optical Path Length— 12.7 cm Reference: The Warner & Swasy Co. (41,44). 76 8. Spectral Absorption Coefficient of Methanol F l a m e .......... 77 9. Monochromatic Black Body Flux T=1200 K°, 1100 K°, 1000 K ° ............ 78 10. Monochromatic Black Body Flux T=1500 K°, 1400 K«, 1300 K ° ............ 79 11. Monochromatic Black Body Flux T=1700 K°, 1600 K“....................... 80 12. Spectral Absorptivity of Methanol Flame .... 89 13. Monochromatic Absorption Coefficient of Methanol F l a m e ................................... 90 14. Monochromatic Volume Emission Coefficients of Methanol Flame........................... 91 15. Spectral Absorptivity of Acetone Flame Optical Path Length— 0.8 c m ............ 100 X Figure Page 16. Monochromatic Absorption Coefficient of Acetone F l a m e ...................................... 101 17. Monochromatic Volume Emission Coefficient of Acetone Flame ............................... 102 18. Monochromatic Flux to Target from a Sheet Flame 0^=17/2, S/D=1; W=0; Methanol; Method 1.................................... 113 19. Monochromatic Flux to Target from a Sheet Flame a=7r/2, P=n/2; S/D=5; W=0; Methanol; Method 1.................................... 114 20. Monochromatic Flux to Target from a Sheet Flame CK=7r/2, j3= ir/2; S/D=10; W=0 ; Methanol; Method 1.................................... 115 21. Monochromatic Flux to Target from a Sheet Flame 0P=^/2, )8= #/2; S/D=1; W=17’/4; Methanol; Method 1..................................... 116 22. Monochromatic Flux to Target from a Sheet Flame (%= V 2 , /3=ff/2; S/D=5; W=7T/4; Methanol; Method I...................................... 117 23. Monochromatic Flux to Target from a Sheet Flame 0!= V2 , /3=ir/2 ; S/D=10 ; W= V4 ; Methanol ; Method 1..................................... 118 24. Monochromatic Flux to Target from a Sheet Flame 0£=if/2, /3=7t/2; S/D=0; W=ff/2; Methanol; Method I.................................... 119 25. Monochromatic Flux to Target from a Sheet Flame Cpff/2, /3=7T/2; S/D=l; W=ir/2 ; Methanol; Method 1 .................................... 120 26. Monochromatic Flux to Target from a Sheet Flame a^1t/2, /3=7T/2; S/D=2; W= V2 ; Methanol; Method 1 ..................................... 121 xi Figure Page 27. Monochromatic Flux to Target from a Sheet Flame 0£=ir/2, j3=ir/2 ; S/D=3; W= V2 ; Methanol; Method 1..................................... 122 28. Monochromatic Flux to Target from a Sheet Flame 05=^/2, P-ïï/2; S/D=4; W=^/2. Methanol; Method I.............................. 123 29. Monochromatic Flux to Target from a Sheet Flame OPff/2, j3=7r/2; S/D=5; W=7t/2; Methanol; Method I............................ 124 30. Monochromatic Flux to Target from a Sheet Flame Of=7r/2, g=7T/2 ; S/D=6 ; W=tt/2; Methanol; Method 1.................................... 125 31. Monochromatic Flux to Target from a Sheet Flame Or=lT/2, /3=ir/2; S/D=7; W=ïT/2; Methanol; Method 1.................................... 126 32. Monochromatic Flux to Target from a Sheet Flame (%=ir/2, jS=ir/2; S/D=8; W=ff/2; Methanol; Method 1.................................... 127 33. Monochromatic Flux to Target from a Sheet Flame Ot=7r/2, 0=#/2; S/D=9 ; W=7t/2; Methanol; Method 1.................................... 128 34. Monochromatic Flux to Target from a Sheet Flame 0^^/2, 0=?/2; S/D=10; W=îT/2 ; Methanol; Method 1...................................
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