Hydrogen explosion is one of the most dangerous accidents in nuclear power plants, which has drawn experts' attention since Fukushima nuclear accident. Plenty of research has been carried out on hydrogen distribution, such as AIHMS program in India, SPARC program in Korea, and CIGMA program in Japan recently, for the purpose of figuring out the hydrogen transport mechanisms and developing simulation codes. Hydrogen up-flow model is one of the important models that initiates the hydrogen source and describes the hydrogen distribution in the centerline of the containment. However, the original model cannot predict the mass fraction of hydrogen precisely and efficiently. In this paper, a one-dimensional up-flow (along with the vertical direction) model has been proposed, in consideration of air resistance and entrainment, which has been inferred from AIHMS test results. This new model is verified by the experimental data from Sandia National Laboratory (SNL) and compared with literature findings, which shows good predictions compared with the original one. Based on the typical Froude numbers, the present optimized model is applied to conditions of typical injection characters. With the help of analyzing the gas velocity, characteristic length of B, nondimensional parameter of z/l(s), and mass fraction of hydrogen, a definition of hydrogen expansion process has been given, which can be quantified and detailed by an proposed explosive expansion criterion. This work can help understand the dominated regime of either buoyancy or momentum and can be employed in simulation codes in the future, for the purpose of quick evaluation in severe accident management and accidents emergency decision.