As technology advances, submarine performances in various aspects, such as speed, diving depth, armament, and propulsion, can be improved. However, the improvement of anti-submarine technology has forced countries to accelerate the development of detecting underwater noise, and the submarine’s underwater concealment has been challenged unprecedentedly [1
]. Therefore, navies and research institutions around the world are working tirelessly to promote the development of submarine quieting technology and have developed a series of noise reduction measures to improve the submarine’s stealth as much as possible. Applying “quieting” technology to submarines has become the mainstream of contemporary submarine development.
The main noise of submarines is divided into two types: radiated noise and self-noise, both of which are generated by the submarine’s noise sources and are closely related. The radiated noise of submarines mainly comes from various mechanical vibrations on the submarine body, propeller rotation, fluid slapping during submarine navigation, and air noise inside the cabin radiating out through the hull, which is detected in the water at a certain distance from the submarine’s surface. In general, mechanical vibration noise and propeller noise account for the majority of radiated noise, while hydrodynamic noise has a significant impact on the submarine’s self-noise. Propeller noise is a major noise source during submarine navigation, because the propeller rotates at high speed, which causes uneven radial loading on the blades, resulting in singing and vibration.
The propeller works at the tail of the submarine; the unevenness of the flow field will cause the propeller blade to emit discrete noise. On the basis of ensuring the maneuverability and safety of the submarine, the design of the rudder on the submarine also needs to consider the uniformity of the submarine’s tail flow field. Currently, the research on submarine rudder mainly focuses on the hydrodynamic performance of the rudder and its effect on the maneuverability of the submarine, while there is less research on the impact of the submarine rudder on the tail flow field. The existence of the rudder makes the flow field at the propeller plane have a strong radial unevenness, which will cause the propeller to oscillate during rotation, causing a loss of hydrodynamics and making the propeller noise increase [2
When the submarine is moving underwater, vortices will be induced on the upper edge of the end surface of tail fin and on the top surface of the body due to flow separation and reattachment. Additionally, "necklace-shaped" vortices will be induced on the body’s leading edge at the location of the horseshoe vortices downstream. The generation of these vortices will certainly affect the uniformity of the flow field at the propeller plane, and when the flow field at the propeller plane is unstable, the noise of the propeller will be higher, and the propulsion efficiency of the propeller will be reduced. Since the distance between the tail control surface and the propeller is relatively close, the flow field at the propeller plane is greatly disturbed, causing the propeller to vibrate when it rotates and resulting in hydrodynamic loss and increased propeller noise [3
]. Du et al. analyzed the vortex distribution in the flow field around the submarine under various conditions. The calculation results indicate that there are vortices at the rear of the four tail fins and the angle between the tail fins, the number, shape, and intensity of the vortices change with the drifting angle and the degree of uniformity of the flow field [6
]. Li et al. changed the shape and arrangement of the submarine tail fins and used computational fluid dynamics (CFD) methods to simulate the tail flow of the submarine. The results show that, for the tail flow field under different layout positions of the cruciform rudder and “X” rudder, the forward movement of the rudder position improves the tail flow field, while the full-body submarine “X” rudder tail control surface reduces the unevenness of the flow field at the propeller plane [7
]. Bai and Lu made significant modifications to the stabilizer wing based on the SUBOFF standard boat model and used CFD methods to conduct an analysis of the impact of the body on the submarine resistance and tail flow field. The stabilizer wing resulted in a significant increase in the submarine’s pressure drag and is also the main reason for the unevenness of the flow field at the propeller plane [8
]. Zhai and Liu studied the tail flow field quality of the co-wing-type rudder and non-co-wing-type rudder under the influence of the hull. The results showed that the co-wing type rudder can significantly reduce the vortex flow at the combination of the rotating rudder and the stabilizer wing and improve the fluid velocity in the low-speed area of the tail flow behind the rudder. At the same time, if the maximum thickness of the local isogonal rudder is reduced, the tail flow field can be further improved, and the rudder force will not be damaged [9
]. Lee et al. studied the tail flow of the cruciform rudder tail control surface and found that the cruciform rudder tail wing produced three vortex systems in the same direction, with the strongest vortex at the wing tip, followed by the leading edge of the wing and, finally, the trailing edge of the wing [11
Some scholars have attempted to improve the tail flow field by designing vortex elimination devices or optimizing tail fins. Zhang et al. [12
] studied the weakening of the vortex by filling the angle and found that installing a filling angle or designing a three-dimensional flowline on the vertical shell can significantly improve the flow quality in the shell region, effectively suppressing the horseshoe vortices. Liu et al. [14
] designed a vortex elimination and straightening plate based on the characteristics of the horseshoe vortices at the main body junction. The vortex elimination and straightening plate is installed in the horseshoe vortex generation area and uses the lateral velocity component generated by the eddy on both sides of the body to produce a “secondary vortex” that is opposite to the horseshoe vortex rotation direction. These two vortices will weaken each other during their downstream development, thereby actively controlling the horseshoe vortex and improving the quality of the propeller inflow.
The sail is the largest appendage on the submarine, especially in the case of large rudder angles; the sail planes (also known as diving planes or forward fins) will have a significant impact on the tail horizontal rudder [18
]. In some submarines, the resistance increment generated by the command center hull accounts for as much as 28% of the total resistance of the bare hull. The sail also affects the stability and uniformity of the submarine’s tail flow field, resulting in high low-frequency discrete noise and low-frequency broadband noise from the propeller. Liu and Huang calculated the azimuthal distribution of the axial velocity and nonuniformity coefficient for different wing types, different chord lengths, and different heights of the sail hull with the main body. Their research shows that appropriately reducing the height of the sail hull and increasing the thickness of the sail hull can make the tail flow field more uniform [19
]. Gorski carried out research on the design of new style of sail hull and conducted wind tunnel tests on the flow field of newly designed sail hull [22
]. Rais-Rohani and others explored the design of enclosure structures using composite materials, but research on the relationship between the tail flow field and vortex characteristics at the joint of the new enclosure has not yet been carried out [23
]. Toxopeus employed CFD methods to study the structure of the typical horseshoe vortices at the connection between the sail hull and the main hull. By changing the shape of the sail hull and adding a smooth transition arc-shaped filling angle (CUFF) at the front of the connection, the formation of horseshoe vortices can be suppressed, thus reducing additional resistance and improving the quality of the tail flow field [24
]. Wang et al. adopted turbulence model of SST k-ω based on Reynolds Average Navier–Stokes (RANS) method to calculate the wake field of three new types of submarine hulls and analyze the development of the junction vortex and the wake field along the hull. The results show that the sail hull with smooth transition of the leading edge changes the distribution of vorticity at the propeller surface, which effectively suppresses the occurrence of tip vortex by improve the wake structure [25
]. Liu et al. and Sheng et al. took SUBOFF as a model to explore the optimization law of the line form of the sail hull. The results show that sail hulls in the shape of sand dunes and the inclined wall can reduce the amplitude of axial velocity fluctuation at the propeller disk surface and improve the uniformity of the wake field [26
]. Zhang et al. proved that the tip leakage vortex is the cause of the pulsating pressure of the pump-jet propeller by studying the spectral characteristics of the pulsating force and pointed out that the uniformity of the flow field has a significant impact on the pulsating pressure [28
]. Su et al. (2022) used the coupled finite element method (FEM) and the direct boundary element method (BEM) to calculate the vibro-acoustic response of the pump-jet shaft-underwater coupling system and studied the influence of the duct (including the distributed pressure on the duct and the vibration transmission characteristics) on the acoustic radiation [29
]. Zhang et al. (2022) used the RANS method to explain the excitation force generation mechanism of submarine thrusters with uniformly spaced and nonuniformly spaced rotor blades [30
]. Hou Xingyu et al. (2023) studied the effect of random turbulence on the broadband unsteady excitation force of submarine thrusters [31
To sum up, scholars carried out plenty of detailed research on the velocity distribution and vorticity distribution of the submarine wake field. However, those studies mostly analyze the influence of the tail rudder form and vortex elimination device on the wake field from a qualitative perspective but not pay attention to the influence on propeller unsteady bearing force. In this paper, the mechanism of vortex elimination by auxiliary wing is revealed. Meanwhile, the effect of vortex elimination device on submarine propeller bearing force reduction is studied from a quantitative point of view.
In this study, the wake field and propulsion performance of the SUBOFF model equipped with DTMB4383 propeller were analyzed utilizing CFD simulations. The commercial software package STAR-CCM+ was used for grid generation and numerical simulations. This paper is organized as follows: Section 2
provides the simulation details. The mesh verification procedures are described in Section 3
. The calculation results are compared and discussed in Section 4
. Finally, the conclusions drawn from this study are summarized, and plans for future research are stated.