Mixing and combustion are the core processes in the operation of the ramjet engine, and the contact line length (2D) or contact area (3D) is an important bridge to analyze the link between mixing and combustion. In this paper, a new formula for calculating the contact area of two components in an arbitrary complex region is proposed, which can analyze the dynamic mixing process of the two components. It can be used to evaluate the mixing efficiency in the dynamic mixing process, the larger the contact area, the higher the mixing efficiency. This paper establishes a new method to evaluate the mixing in ramjet engines based on the Lagrangian coherence structures, and uses this method to study the feasibility of the application of the lobed mixer in ramjet engines. The study shows that the vortex induced by the lobed mixer can significantly increase the contact area between gas and air in the combustion chamber, effectively enhancing the mixing and combustion of gas and air therein. The average mixing efficiency during the operation increased by 11.046% and the combustion efficiency increased by 8.318%.