A Model of Heat Transfer in Rijke Tube Burners

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Abstract
This paper presents a simple velocity transfer function for use in analysing the acoustic characteristics of Rijke Tube burners. The use of the transfer function is first demonstrated for predicting gauze tone amplification of a Rijke Tube burner when the flame/gauze system is situated in the lower quadrant of an entirely open tube. In this case a simpe π/2 phase shift is assumed for the impedance condition across the flame holder or gauze used to anchor the flame. The paper goes on to describe the use of the transfer function for a different practical situation where the lower end of the tube is considered acoustically closed and the blockage of the burner itself is considered to have little effect on the pressure. This simplified acoustic model predicts qualitatively the resonance properties of such a burner. More accurate results are presented from an advanced acoustic model which incorporates the velocity transfer function as well as taking account of non-constant temperature profiles in the upstream and downstream regions. The transfer function is then shown to correctly predict the main modal frequency of a particular Rijke tube burner. Reasonably accurate predictions of the stability limit are also achieved with this more advanced acoustic model

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