## 1 Introduction
In addition, the wind tunnel tests are set up with static steady conditions, with ignoring the dynamic response of the model during emergency ascent. Therefore, it is difficult to predict the roll oscillations of a model on the surface, as well as some excessive roll that occurred in the full-scale trials. Overall, the emergency rising process involves highly nonlinear, complex coupled motions, especially, as the boat becomes lighter, or it speeds up, the response will change. More importantly, the surfacing process of the model is difficult to model based on relevant hydrodynamic coefficients. However, with the development of high performance computing technology, CFD has been a powerful alternative tool that provides direct numerical solutions of submarine space maneuvers, with accounting for unsteady viscous effect [18; 19]. Meanwhile, considerable details about flow characteristics can be obtained through CFD methods with lower costs and higher accuracy, which provides insight into the physics of the problem. In light of the above advantages of CFD methods, various CFD simulation capabilities for submarine maneuvers had been developed by hydrodynamics researchers [20; 21; 22; 23], especially the Reynolds Average Navier-Stokes (RANS) methods coupled with overset grid technology [24; 25]. [PERSON] et al. [20] provided a physics-based computational method for the trajectory prediction of the fully appended SUBOFF model with a propeller. They interactively coupled the numerical solution of the three-dimensional (3D) unsteady RANS equations, which is solved using a multiblock multigrid scheme, with a 6-DOF motion solver. [PERSON] et al. [21] presented 6 DOF RANS simulations validated by steady state and radio controlled free swimming model experiments. Their work achieves the direct simulation of hull-propeller-rudder interaction by solving the unsteady RANS (URANS) flow about a submarine. In addition, [PERSON] et al. (2019) applied dynamic overlapping grids to simulate the flow around a fully appended submarine, while [PERSON] et al. (2019) adopted two approaches to simulate maneuvers of a radio-controlled submarine model, i.e., the direct simulation using dynamic overset technology and the coupled CFD/potential flow propeller solver. Regarding the study of rising stability of submarine using 6 DOF RANS solver, [PERSON] et al. (2019) took the lead to employ CFD method to investigate the rising stability problem, and developed an unsteady 6 DOF RANS capability for simulating submarine rising maneuvers. He established a submarine model with fixed appendages and no propeller, while the hull-propeller-rudder interactions were modeled through some approximation methods. Meanwhile, the submarine model adopted in his study was an envelope model without any permeable regions or flooding holes in the superstructure. Thereby, [PERSON] was unable to take the influence of the drainage process on surface stability into consideration, such that his study simply predicted the behavior of submarine before surfacing. To sum up, to date, it appears that no one has applied the CFD method to study the rising stability of an ascending submarine with moving rudders and a rotating propeller. In the present work, a 6 DOF URANS method coupled with the overset grid technique is developed for the direct numerical simulation of self-propulsion submarine emergency rising. On the other hand, model tests continue to be the most reliable means to validate the accuracy of CFD-based simulations due to the insufficiency of turbulence modeling ability of CFD methods. With regard to experiments that investigate the roll stability of emergency rising, [PERSON] et al. (2019) validated the coupling effect between yaw and roll motions by implementing a set of model tests of submarine emergency rising. [PERSON] pointed out that the excessive yaw deviation is the key factor resulting in excessive roll during buoyant ascent.