## 3 Results and Discussions
### The Self-Propulsion Simulation  
In order to validate the feasibility of direct numerical simulation method for emergency rising simulation of self-propelled submarine, and further analyze the effect of steering rudder on the roll stability in self-propulsion simulation, in this section a self-designed propeller model is coupled with the main hull to conducts emergency rising simulation. The simulation results of the nonpropelled model with steering rudder are compared with the simulation results of the 2 different steering states in the self-propulsion simulation, and the curves shown in Figure 10a-h are obtained. Figure 10: Cont. Compared with the conventional virtual disk method, this paper adopts a propeller model with real geometry, taking into account the interaction among the propeller, the main hull and sterplanes, which improves the accuracy of the simulation results. Figure 10g-h shows the parametric curves during the process of propeller revolution adjustment and initial velocity matching respectively, before the model is released. For obtaining the same initial advancing state as the non-propeller model test, at the beginning of the simulation, the model is set to move at the desired speed in the \(x\)-axis direction. Then the propeller thrust is balanced with the hull resistance by manually adjusting the propeller rpm for several times. According to Figure 10g, the propeller revolutions is gradually adjusted from 240 rpm to 210 rpm, so that the thrust and resistance achieve equilibrium when the initial velocity is maintained at 1.15 m/s. After the model is released, the increase of drag is attributed to the pressure difference between bow and stern caused by the model pitching. When the initial velocity is almost stable, the other five degrees of freedom motions are released to imitate the emergency rising, meanwhile, the propeller speed remains constant during the remaining simulation. Firstly, according to the curves of axial velocity in Figure 10f, except for the peak value, the axial velocity of the self-propeller model is about 20% higher than that of the nonpropelled model during the whole process of emergency buoyancy. Obviously, it is ascribed to the propeller thrust. Furthermore, it can be seen from the enlarged velocity curves that, in the nonpropelled simulation, the velocity decreases slightly in the initial stage after release, while the velocity increases directly for the self-propulsion simulation. Similarly, due to the large axial velocity of the self-propelled model, the maximum pitch angle and incidence angle of the model are reduced by 23% and 8%, respectively, compared with the peak value of the nonpropelled model, as shown in Figure 10a,b. In addition, note that the influence of propeller mass and centroid on the center of gravity of the main hull is not considered in this paper. Therefore, it is acceptable that the model trims stern down in the stable advancing on the free surface, because this does not affect the discussion on course keeping ability and the qualitative analysis about the influence of the propeller. Since the propeller is a left rotary propeller, the model always rolls to the starboard during the underwater rising process due to the propeller torque. For comparison, the roll and yaw angles of the nonpropelled simulation are taken as opposite values. It can be seen from roll angle curves in Figure 10c that, the maximum roll angle is only about 13\({}^{\circ}\) under the condition of steering rudder, which is significantly decreased by 70% than the roll angle in the simulation without steering rudder. Meanwhile, by comparing curves in Figure 10c for roll angle and Figure 10d for drift angle, we can see that they have similar trends. In terms of the above 3 various states, the roll angle increases with the  
Figure 10: Contrast curves of attitudes between CFD and MT in the condition of rudder steering but no propeller. The experimental data in Figure 7 are repeated here for distinct contrasting.