Cross-Correlation of Sound Pressure and Heat Release Rate for Oscillating Flames with Several Frequencies Excited

Abstract

Subject of the note are combustion oscillations in a small laboratory burner with premixed flames. Oscillations of sound pressure, energy conversion and gas velocity were measured simultaneously within the domain of the flame. Having evaluated amplitudes and phase shifts of the various oscillations, it was possible to find by an inspection of the graphical representation how the conditions required for oscillations are fulfilled. The burner shows different forms of vibrations: sinusoidal vibrations with one frequency, superposition of independent frequencies (beats) and harmonic frequencies. A parameter study shows for which circumstances the different forms occur.

For periodic oscillations the experimental data support the known stability criteria (Rayleigh integral). In the case of aperiodic oscillations we propose to replace the Rayleigh integral by a corresponding cross-correlation function of sound pressure and conversion oscillations. It is suggested that the cross-correlation function has; to approach a positive limiting value which has been found for all investigated cases.