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Theoretical Investigation of Unsteady Flow Interactions with a Planar Flame

Theoretical Investigation of Unsteady Flow Interactions with a Planar Flame. Tim Lieuwen and Ben T. Zinn Schools of Mechanical and Aerospace Engineering Georgia Institute of Technology Atlanta, GA. * Research Supported by AGTSR and AFOSR; Dr. Dan Fant and Dr. Mitat Birkan, Contract Monitors.

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Theoretical Investigation of Unsteady Flow Interactions with a Planar Flame

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  1. Theoretical Investigation of Unsteady Flow Interactions with a Planar Flame Tim Lieuwen and Ben T. Zinn Schools of Mechanical and Aerospace Engineering Georgia Institute of Technology Atlanta, GA * Research Supported by AGTSR and AFOSR; Dr. Dan Fant and Dr. Mitat Birkan, Contract Monitors

  2. Acoustic - Flame Interactions Play an Important Role in the Unsteady Behavior of Many Combustion Systems • Combustion Instabilities • Pulse Combustion • Combustion Noise

  3. Premixed Fuel + Air

  4. Past Investigations of Low Frequency Acoustic - Flame Interactions • Interaction of flame sheet with normally impinging acoustic disturbance • B.T. Chu, Fourth Symposium on Combustion, 1953. • Interaction of plane wave with the flame in realistic combustor geometries • Marble and Candel, 17th Symposium on Combustion, 1978 • Yang and Culick, Comb. Sci. and Tech., Vol. 45, 1986 • Fleifel et al., Comb. and Flame, Vol. 106, 1996 • Dowling, J. Fluid Mech., Vol. 346, 1997

  5. Chu’s Investigated Geometry • Infinitely long flame • Normal Disturbances • Accounts for flame response Typical Investigated Geometry in Other Studies • Finite flame • Oblique Disturbances • Wrinkled flame • Multidimensional Acoustic field • Neglect vorticity production • Neglect flame speed response

  6. Investigated Geometry Flame Front Cold Reactants X ( y,t) f Transmitted Wave Reflected Wave q Hot Products Incident Acoustic Wave Convected Vortical and Entropy Disturbances

  7. Assumptions • Thin, infinitely long flame • Uniform, isentropic, low Mach number mean flows • Molecular transport effects neglected • Time harmonic, plane wave disturbances • Results independent of frequency

  8. Equations

  9. Unsteady Solutions

  10. Matching Conditions

  11. Matching Conditions

  12. Flame Response • Flame response enters through flame speed, S1 • S1=f(p1, T1) • Upstream Conditions Isentropic: • Typical values of k for laminar hydrocarbon flames: 0.4 -0.5

  13. Solution • Get 5 linear, algebraic equations for 5 unknown amplitudes: 1) Reflected acoustic wave 2) Transmitted acoustic wave 3) Vortical wave 4) Entropy wave 5) Flame position

  14. 25 20 15 10 5 0 -25 -20 -15 -10 -5 0 5 10 15 20 25 Velocity VectorsPhase: 0 degrees

  15. 25 20 15 10 5 0 -25 -20 -15 -10 -5 0 5 10 15 20 25 Velocity VectorsPhase: 90 degrees

  16. 25 20 15 10 5 0 -25 -20 -15 -10 -5 0 5 10 15 20 25 Velocity VectorsPhase: 180 degrees

  17. 25 20 15 10 5 0 -25 -20 -15 -10 -5 0 5 10 15 20 25 Velocity VectorsPhase: 270 degrees

  18. Effect of Incident Angle on Production of Acoustic Energy - No Flame Speed Response Normalized Energy Production Reflected + Transmitted - Incident Energy = Incident Energy

  19. Effect of Flame Response on Production of Acoustic Energy

  20. Effect of Vorticity ProductionNo Flame Speed Response

  21. Mechanisms of Acoustic Damping by Flame • Excitation of vortical mode acts as important source of acoustic damping • For flame speed Mach number = 0.005, up to 14% of incident acoustic energy is dissipated • Same amount of acoustic damping provided by exit nozzle of combustor with ambient mean flow Mach number = 0.03

  22. Important features of Planar Acoustic - Flame Interactions • In order to determine the acoustic energy production by a flame, must account for: • Excitation of Vorticity • Flame Speed Fluctuations • All acoustic energy produced by unsteady enthalpy flux through flame • Flame area fluctuations have no effects

  23. Future Work • What are additional effects that occur when non planar flames or disturbances interact? • Effects of flame response due to flame curvature, stretch, etc. • Incorporate results into combustion stability models

  24. Supporting Slides

  25. Mechanism of Acoustic Energy Production

  26. Mechanism of Acoustic Energy Production by Flame • Unsteady heat release produced by unsteady enthalpy flux through flame • Energy added to acoustic field when heat release and pressure are in phase

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