A new dual-fluid model considering phase transition and velocity slip was proposed in this paper and the Cunningham correction was used in the droplet resistance calculation. This dual-fluid model was applied to the numerical simulations of wet steam flow in a 2D LAVAL nozzle and in the White cascade respectively. The results of two simulations demonstrate that the model is reliable. Meanwhile, the spontaneous condensing flow in White cascade was analyzed and it infers that the irreversible loss caused by condensation accounts for the largest share (about 8.78% of inlet total pressure) in total pressure loss while the loss caused by velocity slip takes the smallest share (nearly 0.42%), and another part of total pressure loss caused by pneumatic factors contributes a less share than condensation, i.e. almost 3.95% of inlet total pressure. A new dual-fluid model considered phase transition and velocity slip was proposed in this paper and the Cunningham correction was used in the droplet resistance calculation. This dual-fluid model was applied to the numerical simulations of wet steam flow in a 2D LAVAL nozzle and in the White cascade respectively. The results of two simulations demonstrate that the model is reliable. Meanwhile, the spontaneous condensing flow in White cascade was analyzed and it infers that the irreversible loss caused by condensation accounts for the largest share (about 8.78% of inlet total pressure) in total pressure loss while the loss caused by velocity slip takes the smallest share (nearly 0.42%), and another part of total pressure loss caused by pneumatic factors contributes a less share than than condensation, ie almost 3.95% of inlet total pressure .