Featured Application: The results in this research can provide technical support for the rudder control of a real submarine to suppress the excessive roll of emergency rising. The results also laid the foundation for further research of a free-running submarine model. Abstract: A direct numerical simulation method based on Reynolds Average Navier-Stokes (RANS) equations is used to carry out numerical prediction studies of submarine emergency rising in this paper. Firstly, a numerical simulation of the nonpropelled model without rudder manipulating is accomplished as the basis of this study. The numerical prediction results are in good agreement with the experimental data, which proves the feasibility and accuracy of the direct numerical simulation method. Meanwhile, both model tests and numerical simulation results reveal the strong coupling effect between roll and yaw motions during the underwater ascending process. Based on the above observation and analysis, another two numerical simulations, whose grids are identical with the non-manipulation simulation, are conducted respectively under the condition of rudder steering, i.e., course keeping simulation and self-propulsion simulation. An optimized S surface controller based on conditional determination is designed to manipulate the rudders. As a result, the yaw angle of the latter two simulations is limited within the range of 0.2 • and 0.8 • respectively, proving the effectiveness of the S surface controller. Correspondingly, the maximum roll angle is reduced by 96% and 70% respectively, which demonstrates that the roll stability is significantly enhanced by improving the course keeping ability of the model. Moreover, it is also proven from the perspective of reverse verification that, the excessive yaw deviation is the root cause of emergency rising roll instability for the situation of incidence angle lower than 30 • .Appl. Sci. 2019, 9, 3285 2 of 26 surface. Moreover, Watt [3] also showed how important other variables e.g., yaw and roll etc., are to the stability of the ascent motion, henceforth referred to as "rising stability".In the study on emergency rising stability, previous researchers mainly focused on obtaining the hydrodynamic coefficients through physical captive model tests or numerical simulated captive model tests, then combining the 6 degrees of freedom (DOF) motion equations to carry out maneuverability prediction. Feldman et al. [4][5][6] performed a series of captive model experiments to investigate the stability and control characteristics of submarines, such as straightline towing, rotating arm test etc. Pan et al. [7,8] conducted the numerical prediction of submarine hydrodynamic coefficients and rotary derivatives using the Computational Fluid Dynamics (CFD) approach based on the standard equations of motion for submarine maneuvers [9]. In addition, Booth [10] carried out a classical stability analysis of a nonpropelled submarine by introducing nonlinear incidence terms to conventional coefficient modeling. Booth pointed out the latera...