The intake of ice crystals by an aero-engine is prone to internal icing， causing loss of engine thrust and， in serious cases， aviation accidents. The numerical simulation of ice crystal icing is an important tool to study ice crystal icing， and the calculation of the collection coefficient is a key part of the numerical simulation of ice crystal icing. Based on the NNWICE platform， the numerical simulation and calculation of the drag coefficient， motion trajectory and collection coefficient of ice crystal icing in the early stage of ice crystal icing is carried out， and the accurate calculation of ice crystal collection coefficient based on Monte Carlo method is achieved. Therefore， the coupled numerical calculation method of ice crystal particle motion and heat and mass transfer under Lagrangian framework is developed； by completing the relevant calculation cases of two-dimensional NACA0012 airfoil， the effects of different drag models and ice crystal phase transition on the impact collection coefficient are compared and analyzed. The results show that the drag model has a little effect on the ice crystal collection coefficient， while the ice crystal phase transition will have a significant effect on the ice crystal motion trajectory and collection coefficient， which lays the foundation for further development of the numerical simulation calculation method of ice crystal icing.