Calculation of the stationary flame propagation velocity by the variational principle of irreversible thermodynamics

Abstract

Numerical algorithm for the prediction of the stationary flame propagation velocity over premixed gas mixture has been formulated by using the foundations of non-equilibrium thermodynamics. Considering the combustion as a set of irreversible processes, the steady-state regime of flame propagation is identified with the stationary state of the non-equilibrium thermodynamic system. The generalized form of functional has been stated allowing its minimization relatively to the sought stationary flame propagation velocity treated as additional variable. Based on this variational statement an integral relationship for the flame propagation velocity has been obtained. The calculations of the stationary flame propagation velocity over model premixed gas mixture performed by proposed algorithm showed a faster convergence at the initial steps of iteration process in comparison with the commonly used approach based on the mass conservation of combustion chemical traction. The combined algorithm has been formulated, which benefits from the proposed ‘thermodynamic’ approach at the initial steps and converges to final solution satisfying the general mass balance.