1. 1 A Time-Scale Analysis of Opposed-Flow Flame Spread – The Foundations Subrata (Sooby) Bhattacharjee Professor, Mechanical Engineering Department San Diego State University, San Diego, USA

2. 2 Acknowledgement Profs. Kazunori Wakai and Shuhei Takahashi, Gifu University, Japan Dr. Sandra Olson, NASA Glenn Research Center. Team Members (graduate): Chris Paolini, Tuan Nguyen, Won Chul Jung, Cristian Cortes, Richard Ayala, Chuck Parme Team Members (undergraduate): Derrick, Cody, Isaac, Tahir and Mark. ( Support from NASA and Japan Government is gratefully acknowledged )

3. 3 Overview What is opposed-flow flame spread? Flame spread in different environment. Mechanism of flame spread. Length scales and time scales. Spread rate in normal gravity. Spread rate in microgravity The quiescent limit

4. 4 Upward or any other flow-assisted flame spread becomes large and turbulent very quickly. Opposed-flow flame spread is also known as laminar flame spread.

5. 5 AFP: = 0.08 mm = 1.8 mm/s Downward Spread Experiment, SDSU Combustion Laboratory PMMA: = 10 mm = 0.06 mm/s

6. 6 Gravity Level: 1.e-6g Environment: 50-50 O 2 /N 2 mixture at 1.0 atm. Flow Velocity: 50 mm/s Fuel: Thick PMMA (Black) Spread Rate: 0.45 mm/s mm Sounding Rocket Experiment Spread Over PMMA: Infrared Image at 2.7 

7. 7 Fuel: Thin AFP, =0.08 mm = 4.4 mm/s Thick PMMA Image sequence showing extinction Vigorous steady propagation. Experiments Aboard Shuttle: O2: 50% (Vol.), P=1 atm.

8. 8 Mechanism of Flame Spread Fuel vapor O 2 /N 2 mixture The flame spreads forward by preheating the virgin fuel ahead. Virgin Fuel

9. 9 Mechanism of Flame Spread O 2 /N 2 mixture The rate of spread depends on how fast the flame can heat up the solid fuel from ambient temperature to vaporization temperature. Virgin Fuel Vaporization Temperature,

10. 10 Forward Heat Transfer Pathways: Domination of Gas-to-solid Conduction (GSC) Preheat Layer Pyrolysis Layer Gas-to- Solid Conduction Solid-Forward Conduction The Leading Edge

11. 11 Gas-phase conduction being the driving force, The Leading Edge Length Scales

12. 12 Length Scales - Continued

13. 13 Heated Layer Thickness – Gas Phase

14. 14 Heated Layer Thickness – Solid Phase

15. 15 Vaporization Temperature, Ambient Temperature, Energy Balance: Characteristic Heating Rate Sensible heating (sh) rate required to heat up the unburned fuel from to Heating rate due to gas-to-solid (gsc) conduction: Flame Temperature,

16. 16 Conduction-limited or thermal spread rate: Flame Temperature, Thick Fuel Spread Rate from Energy Equation Vaporization Temperature, For semi-infinite solid,

17. 17 Conduction-limited spread rate: Flame Temperature, Vaporization Temperature, For thermally thin solid, Thin Fuel Spread Rate from Energy Equation

18. 18 Solid Forward Conduction (sfc) Gas to Solid Conduction (gsc) Gas to Environment Radiation (ger) Gas to Solid Radiation (gsr) Solid to Environment Radiation (ser) Parallel Heat Transfer Mechanisms

19. 19 Gas to Environment Radiation (ger) Time Scales Relevant to Gas Phase Available Time

20. 20 Time Scales Relevant to Gas Phase: Thermal Regime Available Time in Gas Phase Gas to Solid Radiation (gsr) Solid to Env. Radiation (ser)

21. 21 Time Scales Relevant to Solid Phase Available Time

22. 22 Time Scales Relevant to Solid Phase: Thermal Regime Available Time

23. 23 The Thermal Regime Governing Equation

24. 24 Gas to Solid Conduction (gsc) The characteristic heat is the heat required to raise the solid-phase control volume from to. Gas-to-surface conduction time: Time Scales – Gas to Surface Conduction

25. 25 Gas to Solid Conduction (gsc) Substitute the two limits of Thermal Regime: Spread Rates Using Time Scales

26. 26 Solid Forward Conduction (sfc) Gas to Solid Conduction (gsc) Relative dominance of GSC over SFC

27. 27 Solid Residence Time: Gas to Solid Conduction (gsc) Solid to Environment Radiation (ser) The radiation number is inversely proportional to the velocity scale. In the absence of buoyancy, radiation can become important. Radiative Term Becomes Important in Microgravity

28. 28 Gas to Solid Conduction (gsc) Solid to Environment Radiation (ser) Include the radiative losses in the energy balance equation: Algebraic manipulation leads to: Spread Rate in the Microgravity Regime

29. 29 Mild Opposing Flow: Computational Results for Thin AFP As the opposing flow velocity decreases, the radiative effects reduces the spread rate

30. 30 Mild Opposing Flow: MGLAB Data for Thin PMMA

31. 31 Gas to Solid Conduction (gsc) Solid to Environment Radiation (ser) The minimum thickness of the heated layer can be estimated as: All fuels, regardless of physical thickness, must be thermally thin in the quiescent limit. The Quiescent Microgravity Limit: Fuel Thickness

32. 32 Gas to Solid Conduction (gsc) Solid to Environment Radiation (ser) The spread rate can be obtained from the energy balance that includes radiation. where, The Quiescent Microgravity Limit: Spread Rate reduces to:

33. 33 In a quiescent environment steady spread rate cannot occur for The Quiescent Limit: Extinction Criterion

34. 34 Extinction criterion proposed is supported by the limited amount of data we have acquired thus far. The Quiescent Limit: MGLAB Experiments

35. 35 A phenomenological model for opposed flow flame spread is built around two residence times, one in the gas phase and one in the solid. Theoretical solutions in the thermal regime are reproduced using the time scale analysis. Deviation from the thermal regime can be quantified by comparing the time scale of the added physics with the appropriate residence time. In the quiescent microgravity environment all fuels behave like thin fuels. A critical thickness is proposed beyond which a spreading flame cannot be sustained in such environment. Conclusions