# Effect of Waves on the Behavior of Emergent Buoyantly Rising Submarines Using CFD
## 1 Introduction  
A submarine must rise to the water surface quickly in emergency situations; the most efficient way is to blow the ballast tanks, making the submarine acquire excess buoyancy and rising velocity. However, an emergent buoyantly rising submarine encounters the problem of a large trim angle, especially excess roll. Full-scale trials found that the roll angle of an emergent buoyantly rising submarine could be above 25\({}^{\circ}\)[1]; a model test found that it could even exceed 60\({}^{\circ}\). For the safety of the crew and equipment on a submarine, it is critical to analyze the behavior of emergent buoyantly rising submarines to decrease the maximum roll angle.  
Early studies on the behavior of an emergent buoyantly rising submarine were conducted using quasi-steady coefficient-based simulations [1; 2; 3; 4]. [PERSON] found that the maximum roll angle was considerably sensitive to the initial roll angle and predicted an emergence roll angle of 9\({}^{\circ}\) with an initial heel angle of 2\({}^{\circ}\). When the submarine had no initial heel angle, the emergence roll angle wasonly \(1.5^{\circ}\), which does not agree with the actual situation. In addition, the coefficient method consists of uncertainties.  
A submarine is assumed to sail in deep and broad waters when evaluating these coefficients; the flow in the casings is not considered. However, the velocity in the casings of an emergent buoyantly rising submarine is significant, and the flow in the casings affects the behavior of the submarine. When a submarine sails near the water surface, the coefficients are significantly affected; however, this is not considered when calculating coefficients. Hence, these coefficients cannot be used to predict the behavior when a submarine emerges and oscillates on the water surface. In addition, the nonlinear effect of an emergent buoyantly rising submarine is substantial; however, the coefficients can barely model the consequent unsteady effect.  
Conducting a model test is the most effective method for studying the behavior of emergent buoyantly rising submarines. The Harbin Engineering University conducted a series of experiments to analyze the effect of each initial condition on the behavior of emergent buoyantly rising submarines, but did not investigate the effect of waves [5; 6]. Moreover, a model test is very costly and time-consuming.  
The computational fluid dynamics (CFD) method requires less cost and time, and the flow details (such as velocity, pressure, and vorticity) can be acquired; thus, this method is widely used in fluid mechanics. [PERSON] [7] analyzed the rising stability problem using six-degree-of-freedom Reynolds average Navier-Stokes (RANS)-based simulations in which the disadvantages of coefficients were ignored when modeling the hydrodynamic loads that acted on submarines. However, the effect of casings or flooding holes was not considered; thus, the simulations could not predict the surge of water from the holes when a submarine emerged and oscillated on the water surface. Therefore, only the behavior of an emergent buoyantly rising submarine prior to surfacing was predicted. The CFD simulation conducted by [PERSON] et al. [8] considered the effect of casings and flooding holes. The predicted results were in good agreement with the experimental results; however, the effect of waves was not analyzed. In this study, the effect of waves on the behavior of emergent buoyantly rising submarines was investigated using the CFD method. The types of waves include the head wave, following wave, beam sea, and oblique waves. Both the submarine model and the CFD method employed in this study are the same as those employed by [PERSON], except for the simulation of waves.