## 5 Analysis of Results  
Analysis of Watershed Flow Field Characteristics of Pump-Jet Vector Thrust Submarine During Oblique Navigation  
The pump-jet vector thrust submarine exhibits longitudinal and lateral velocities during sideslip motion. By rotating the submarine hull, a sideslip motion model is established under different drift angles, as shown in Figure 7. Numerical simulations are conducted for sideslip motion at drift angles of \(3^{\circ}\), \(5^{\circ}\), \(7^{\circ}\), and \(9^{\circ}\) under rotational speeds of 1500 rpm, 2000 rpm, 2500 rpm, and 3000 rpm for the pump-jet vector thrust submarine. The study analyzes the flow characteristics under different speeds and drift angle conditions. Figure 8 shows the pressure and velocity cloud maps in the flow field after 1.2 s of oblique motion under a drift angle of \(3^{\circ}\) with the screw mixed-flow pump operating at rotational speeds of 1500, 2000, 2500, and 3000 rpm. During the forward motion of the pump-jet vector thrust submarine, it experiences a reaction force from the liquid. High-pressure zones are generated at the bow, the cross-type stern, and the incident surface of the screw mixed-flow pump due to the action of the liquid, and viscous solid-liquid interactions lead to the formation of a localized positive pressure region at the bow, as indicated by A in Figure 8. Additionally, the viscous interactions affect the liquid motion around the hull, creating localized high-velocity regions at the bow, the front of the rudder, and the stern of the submarine. Under high-speed operating conditions, the incident surface experiences more significant resistance, resulting in an increase in pressure on the incident surface. Correspondingly, due to the reduced diameter of the rotating body at the rear of the underwater vehicle, the speed increases on both sides of the vessel, and with the increase in the driver's rotational speed, the acceleration at the rear of the hull becomes more pronounced. The velocity and range of the pump-jet flow tail significantly improve. In the middle section of the pump shell of the screw mixed-flow pump, pressure fluctuations arise due to changes in shell curvature, resulting in a relatively low-pressure zone, as shown in Figure 7 by label 2. Figure 6: Correlation data ((**A**): \(V\) and \(n\); (**B**): \(R\) and \(V\)). To investigate the influence of drift angles on the fluid domain dynamics during sideslip motion, the rotational speed of the spiral mixed-flow pump is set to the design speed (1500 rpm). Different geometric models are constructed for varying drift angles to numerically study the pressure and velocity distribution patterns around the vessel at different drift angles. Figure 8 depicts pressure and velocity contour plots for the submarine during sideslip motion at drift angles of \(3^{\circ},5^{\circ},7^{\circ}\), and \(9^{\circ}\). Since the pressure around the hull arises from the interaction between the hull and the fluid, the solid-liquid interaction mechanisms remain consistent across different drift angles, leading to minimal effects on the pressure distribution in the sideslip motion regime. Figure 8: The effect of rotational speed on the pressure and velocity around the ship. Figure 7: Conceptual diagram of drift angle. The liquid flow velocity around the hull originates from the viscous action of the solid walls on the liquid. Changes in the drift angle similarly do not impact the viscous interaction mechanism. During sideslip motion processes, regions near the bow of the submarine (denoted as point A in Figure 9), the rudders (marked as point B in Figure 8), and areas near the spiral mixed-flow pump (labeled as point C in Figure 9) exhibit nearly identical high-speed distribution regions. As the fluid flows past the bow of the submarine and the leading edges of the cruciform rudder, the velocity rapidly increases and propagates rearward.