The Royal Netherlands Navy (RNN) operates four diesel-electric submarines, the Walrus class. The submarines sail submerged on electric engines and periodically recharge the batteries with diesel engines at periscope depth. The exhaust gases are dispelled at the back of the sail below water level. During the sea trials it was observed that the rising exhaust gases elevated the surface locally with a height of 1 to 2 m. This elevation limited visibility through the periscope, water flooded the air intake and the submarines could be easily detected. To remedy this problem model tests were performed. To enable evaluating several exhaust configurations for a replacement of the Walrus class a numerical model is studied to predict the surface elevation. To model this situation a numerical method is used. The method applied in this work is the Volume of Fluid code ReFRESCO, which is a Reynolds Averaged Navier-Stokes (RANS) solver. Three test cases are studied, a rising bubble, a buoyant jet and an exhaust plume from a submarine sail. The simulations for the buoyant jet show that the momentum in the jet is dominated by buoyancy rather than by the initial inflow momentum. The influence of different turbulence models on the width of the jet and the corresponding surface elevation are investigated. The choice of turbulence model influences the distribution of air in the domain, but does little to the surface elevation. It is concluded that the KSKL model yields the most physical results where the air spreads out in the domain. This model also has a satisfactory convergence behavior. It is concluded that both the density of the exhaust gas and the velocity profile at the nozzle have little influence on the final result. A parabolic velocity profile instead of a uniform outflow does improve the convergence. The dominant numerical error is the discretization error, which is in the order of 12% for the surface elevation. To this end the L∞ norm of the iterative error must be reduced to a satisfactory value, in the order of 10^-3 or smaller. Comparing the results with experiments is difficult due to a lack of proper experimental data, however it is concluded that the results are in a similar order of magnitude. Finally the exhaust gases on a submarine sail are modeled. For the modeling three simplifications are made: only the flow surrounding the sail is modeled (the hull of the submarine is not modeled), the control planes on the sail are not modeled, and no incoming waves on the free surface are taken into account. Both in the experiments and in the simulations a pulsating behavior can be observed in the rising air. L∞ norms for the submarine modeling are generally in the order 10^-3, but occasionally less. The numerical results are validated against the experimental results. It is concluded that the use of the RANS code ReFRESCO is possible for the modeling of a submerged exhaust of a submarine. The estimated uncertainty for the result is in the order of 15%.