Transfer Function Calculations for Aeroengine Combustion Oscillations

Combustors with fuel-spray atomizers are particularly susceptible to a low-frequency oscillation at idle and subidle conditions. For aeroengine combustors, the frequency of this oscillation is typically in the range 50–120 Hz and is commonly called “rumble.” The mechanism involves interaction between the plenum around the burner and the combustion chamber. Pressure variations in the plenum or the combustor alter the inlet air and fuel spray characteristics, thereby changing the rate of combustion. This in turn leads to local “hot spots” which generate pressure oscillations as they convect through the downstream nozzle. In order to eliminate the combustion oscillations, it is essential to determine which fuel atomizers are particularly likely to lead to instability by quantifying their sensitivity to flow perturbations. This can be done by identifying the system through understanding the transfer function, which represents the relationship between the unsteadiness of combustion and the inlet fuel and air. In the present work, various types of signals are applied to produce a small change in the inlet fuel and air flow rates, the response in the rate of heat release caused downstream was calculated and stored for subsequent analysis. Afterwards, the system transfer function is calculated by determining the coefficients of an IIR filter (Infinite Impulse Response) for which the output signal is the downstream heat release rate and the input signal is the inlet flow rate. The required transfer function then follows from the Fourier transform of this relationship. The resulting transfer functions are compared with those obtained by the forced harmonic oscillations at a fixed given frequency. Suitably chosen input signals accurately recover the results for harmonic forcing at a single frequency, but also give detailed information about the combustor response over a wide frequency range. There are two distinct forms to the low-frequency quasisteady response. In the primary zone, the rate of combustion is influenced by the turbulence and is enhanced when the inlet air velocity is large. Near the edge of combustion zone, the rate of combustion depends on the mixture fraction and is high when the mixture fraction is close to the stoichiometric value. This generates ‘hot spots’ which convect into the dilution zone. At higher frequencies, the combustion lags this quasi-steady response through simple lag-laws and the relevant time delays have been identified.