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• Algorithm for PLIC-based interfacial area concentration on 3D non-orthogonal grids. • Thermal phase change model with geometrical basis and free of empirical input. • Oscillating behavior of GOX jet plume in LOX crossflow is reproduced in simulation. • Imbalance between the mass transfer rate and the supply causes the oscillation. • Methodology developed is verified by the Stefan problem and the bubble experiment. In order to enhance the physical basis of the mass transfer model in numerical simulation of gas-liquid direct contact condensation and improve the fidelity, a set of methods and models are developed. Based on the concept of the piecewise-linear interface calculation (PLIC), an interface reconstruction algorithm is proposed to calculate the interfacial area concentration in three-dimensional non-orthogonal structured grids. The actual interface in the cell is replaced by a plane, whose position is determined iteratively to satisfy the local volume fraction and orientation of the actual interface. The area of the polygonal cut by the plane is taken as the interfacial area in the cell. The proposed algorithm is validated by calculating the surface area of a series of basic geometries. Obvious superiority of the proposed algorithm over the traditional models (gradient model and algebraic model) is seen. Then, the reconstructed area is used to determine the interfacial area concentration in the thermal phase change model. The process is implemented by ANSYS Fluent user-defined functions. The Stefan problem and steam bubble condensation experiment are used to test the performance of the developed methods and models. The simulation results agree well with the theoretical and experimental results with the quantitative relative errors no more than 4.3 % and 15 %, respectively. The oxygen jets condensation experiments are also used as test cases. The primary dominant frequencies predicted by the simulations are 163.01 Hz and 131.65 Hz, which agree well with the 139.72 Hz and 125.75 Hz in the experiments. The relative errors are only 17 % and 4.7 %. The unstable flow pattern of oxygen jet in liquid oxygen crossflow is explained based on the dynamic characteristics of turbulence, heat and mass transfer. The periodic variation of mass transfer rate is considered as the cause of condensation oscillation. The method for calculating the interfacial area proposed in this paper can serve as an optional and practical improvement to the numerical simulation of direct contact condensation. [ABSTRACT FROM AUTHOR]