Thermo-acoustic flame instability criteria based on upstream reflection coefficients

A prospective method to assess thermo-acoustic instabilities based on two reflection coefficients measured from the upstream side of the burner is presented and experimentally validated. In order to compose a model which allows predicting the onset of thermo-acoustic instability of combustion in a practical appliance, one has to characterize the thermo-acoustic properties of the burner including the flame as an acoustically active element and acoustic properties of all other (usually passive) components of the combustion appliance both upstream as well as downstream of the burner. This kind of modelling strategy usually faces serious practical problems related to the need of measurements/modelling at the hot downstream part of the system. In the present work, we propose a measurement and a system modelling approach which relies on two acoustic measurements, namely reflection coefficients, only at the cold (burner upstream) part of the combustion appliance. Both reflection coefficients, termed upstream and input, can be readily measured using standard acoustic techniques. The need to measure the input reflection coefficient of an acoustically active subsystem may impose difficulties related to the acoustic instability of the measurement setup itself. The approach and technical solution to handle this problem via a special modification of the excitation source (loudspeaker box) is proposed. The dispersion relation to search for system eigen frequencies is represented in a form that couples the reflection coefficients of the upstream part of the appliance and input reflection coefficient from the downstream part as observed through the burner with flame. This form of the dispersion relation is commonly used in the theory of radio-frequency circuits and recently introduced for thermo-acoustic problems. The proposed method is applied to burners with premixed burner-stabilized Bunsen-type flames. The observed instability conditions and oscillation frequencies are compared with predictions of the proposed modelling approach and reveal good correspondence.