Abstract:
The numerical simulation of chemical non-equilibrium flow contains solving the governing equations of flow and chemical kinetics. Point-implicit and fully implicit methods, involving the matrix inversion calculations, require great computational costs in solving the stiff ordinary differential equations that limits their applications in complex engineering problems. To solve this problem, Liu proposed a novel uncoupled method for chemical non-equilibrium flow in 1993, the governing equations are decomposed into two parts of flow and chemical reaction. A frozen flow model is used in flow equations to describe the motion of fluid, and the solution of chemical reaction equations describe the explosion process in adiabatic and source equations are employed to simulate chemical reaction process in the local adiabatic and constant volume thermodynamic system. By combining Liu's uncoupled method with the space mean character of finite volume method, the present study introduces an optimization flow equation method, which only resolves the partial differential equations with five variables. These equations have the same form as calorically perfect gas equations. The optimization method can significantly improve the computational efficiency. In addition, the authors first use the precise time-integration method in solving the stiff ordinary differential equations. Compared with the VODE and α-QSS methods, the precise time-integration method has better numerical stability and is insensitive to time step. Therefore, the advantage of precise time-integration method on solving the stiff ordinary differential equations can be prominent by selecting a proper time step.