Simulation of combustion – Acoustic interactions using a conjugate method

A modern approach of conjugate problem formulation currently widely used in heat transfer theory and applications is applied to simulate combustion–acoustic interaction process. The term conjugate corresponds to problems when solution domain consists of two or more subdomains with different properties and/or with phenomena described by different type of differential equations. In heat transfer, such subdomains are usually a fluid and a body or two fluids separated by solid. Similarly in combustion, such subdomains are fresh and burnt gases divided by a flame. As an example, the effect of flame location and burnt/fresh gases temperature ratio on combustion stability is investigated. It is assumed that forced oscillations are imposed on an existing in a tube flow, and stability of final oscillations at different flame locations and temperature ratios is studied. The well-known simple one-dimensional approach is improved using a physically founded, more reliable combustion model and an alternative method of solution based on strict mathematical formulation as a boundary-value problem similar to that applied in conjugate heat transfer theory. The mathematical development leads to a system of two integro-differential equations determining final velocity and pressure amplitudes at the flame. Analysis of an exact solution of this system gives the domains of similarity parameter defining time lags of the imposed forced oscillations that theoretically provide stability of the final oscillations. The stability pattern shows that the value of time lag decreases with increasing both parameters flame distance from the tube entrance and burnt/fresh temperature ratio.