Impact of flame base dynamics on the non-linear frequency response of conical flames

Abstract

The response of laminar premixed conical flames to velocity disturbances is considered theoretically and experimentally with a focus on the impact of the flame base dynamics on the non-linear behavior of the Flame Transfer Function (FTF). Unsteady heat transfer between the flame base and the burner lip is considered to model the flame base response. Predictions for the flame base response <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>Ξ</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>ω</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:math> and flame transfer function <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>F</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>ω</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:math> are compared to measurements over a large range of frequencies. The non-linear behavior of the FTF phase is shown to result from a competition between velocity disturbances contributing to a regular increase of the phase lag with frequency and flame base oscillations leading to a saturation of the phase lag at high frequencies. Increasing the forcing level leads to an early saturation of the phase lag of the FTF at lower frequencies. This analysis demonstrates the important role of flame foot oscillations controlling the saturation of the FTF phase lag.