1. Introduction
Oceanic resource development and utilization play a vital role in sustainable economic and social progress. Autonomous underwater vehicles (AUVs) have emerged as significant tools for ocean exploration due to their intelligence, cost-effectiveness, high efficiency, and suitability for complex environments. To meet the needs of seafloor resource exploration, AUVs are used in tasks such as seafloor mapping, offshore oil and gas exploration, and subsea pipeline inspection and maintenance [
1,
2]. In such cases, AUVs need to operate in close proximity to the seafloor, and the existence of submarine boundaries makes the flow field around an AUV different from that in infinite waters [
3], thus affecting the AUV’s hydrodynamic performance and interfering with its maneuvering performance. For example, studies have highlighted phenomena like swaying and pitching as AUVs approach the seafloor [
4], and Kim [
5] reported the measurement inaccuracies caused by the pitching motion of AUVs and indicated that interference from the seafloor boundary influences the operational efficiency and safety of AUVs, making it essential to consider its effects for ensuring stability, enhancing detection accuracy, and expanding operational scenarios.
Given the high costs and limitations of physical model experiments, research on AUV fluid dynamics often relies on cost-effective and accurate simulation techniques. Many studies neglect boundary conditions, but AUV hydrodynamic performance is particularly sensitive to them. Research by Kuang et al. [
6] used computational fluid dynamics (CFD) to simulate submarine near-seafloor towing experiments, which revealed changes in submarine hydrodynamics and established linear relationships between certain hydrodynamic parameters and the ratio of submarine diameter to distance from the seafloor (
D/
H) and attack angle. They suggest that unmanned underwater vehicles (UUVs) traveling with small positive attack angles could counteract some of the seafloor suction effects. Building on this, Wu et al. [
7] studied the water dynamics of a submarine model (SUBOFF) near the seafloor and concluded that certain hydrodynamic components of submarine motion present good linear relationships with the square of the inverse dimensionless distance from the seafloor (
D/
H)
2. Similarly, Du et al. [
8] analyzed the impact of the seafloor on unmanned underwater vehicles (UUVs) and obtained a critical distance from the seafloor where UUVs are less affected by seafloor interference. Korol et al. [
3] extended these results by determining the distance from the wall where maximum resistance occurs and noting that in the limit of small wall distances, boundary layer flow induces a decrease in velocity and frictional resistance. Zhu et al. [
9] conducted underwater vehicle zero-angle-of-attack towing experiments at different distances from the seafloor and concluded that interference from the seafloor can be neglected when the distance is greater than a quarter of the vehicle length. Chen et al. [
10] calculated additional mass for underwater helicopters near the seafloor using the panel method and established a linear relationship between additional mass and distance from the seafloor. Wu et al. [
11] analyzed the unsteady hydrodynamic interference between an underwater self-propelled AUV and the seafloor using the CFD method and reported the critical conditions under which the AUV was affected.
In the above studies, the seafloor boundary is regarded as a flat wall, and the phenomena of increasing resistance and negative lift of underwater vehicles near the flat seafloor are mainly analyzed, as well as linear relationships between hydrodynamic parameters and cruising height and attack angle. However, the actual seafloor terrain is diverse, and complex flow fields induced by complex seafloor terrains have a profound effect on AUV stability. Certain studies have focused on the effects of complex seafloor terrains on underwater vehicles. Liu [
12] simulated towing experiments of AUVs near the seafloor using the CFD method and investigated changes in AUV hydrodynamics in the process of navigating above typical complex terrains such as single inclined slopes, seafloor bedrock terrains, sand wave terrains, and eroded depression terrains. Yan et al. [
13] numerically investigated the influence of downward slopes on the hydrodynamic performance of nearby AUVs using the CFD method. Mitra et al. [
14] conducted water tank experiments and numerical simulations of the Reynolds stress model to study the forces acting on AUVs above a wedge-shaped seafloor. They analyzed hydrodynamic values such as resistance, pressure, and friction coefficients for AUVs under different Reynolds numbers, attack angles, and drift angles, which provided insights for designing and improving AUVs for operations above continental slopes and in estuaries. Guo et al. [
15] studied the influence of an inclined seafloor on an autonomous underwater helicopter (AUH) using the CFD method and suggested that an inclined seafloor has a more significant influence on AUV resistance compared to a flat seafloor.
In the research on the influence of submarine terrains on underwater vehicles, scholars have mainly considered the state of underwater vehicles in relatively stable flow fields. For flow fields characterized by higher turbulence levels, Mitra et al. [
16] excited turbulence using grids and investigated its effects on AUV hydrodynamic characteristics. Similarly, Mitra et al. [
17] explored the influence of rotational flow fields induced by propellers on the changes in hydrodynamic characteristics of AUV. However, these studies primarily focused on the average hydrodynamic characteristics of AUVs, not the turbulent flow induced by complex seafloor terrains over time, which can cause continuous changes in the hydrodynamic characteristics of AUVs, even leading to significant fluctuations in the forces acting on them. Therefore, based on practical engineering considerations, this paper selects common underwater dune terrains, uses the CFD method to simulate turbulent flow near the terrain, and analyzes the hydrodynamic performance and flow field variations in AUVs within the turbulent flow induced by the seafloor terrain, providing a theoretical foundation for AUV maneuverability and control.
3. Results and Discussion
This study focuses on the instantaneous variation in hydrodynamic coefficients of an AUV within the turbulent flow induced by underwater dune terrain. Considering computational efficiency and the full development of the flow field, the simulation time is set to the duration required for the incoming flow to pass twice the length of the computational domain. The chosen incoming flow velocities are , , and . Notably, due to the more pronounced flow variations at the velocity of , the simulation time is extended to the duration required for the incoming flow to pass four times the length of the computational domain at this velocity. The computational results reveal that, during the initial phase when the incoming flow passes one length of the computational domain at the set velocity, the variation in the AUV’s hydrodynamic coefficients remains relatively stable. In other words, the flow field stays in a relatively stable state without reaching full development. Thus, this study analyzes the variation in the AUV’s hydrodynamic coefficients during the subsequent time intervals beyond this stage.
When
, the instantaneous variation in the hydrodynamic coefficients of the AUV at different incoming flow velocities is shown in
Figure 7. It can be observed that the hydrodynamic coefficients of the AUV are influenced by the turbulent flow field and fluctuate within a certain range. As the flow velocity increases, the fluctuations become more pronounced. Regarding the total resistance coefficient, which is divided into the shape resistance coefficient and friction resistance coefficient, it becomes apparent that the fluctuation in the shape resistance coefficient is more intense. Moreover, the variation trend in the shape resistance coefficient aligns completely with that of the total resistance coefficient. This suggests that the changes in the AUV’s total resistance are primarily driven by variations in the shape resistance, while the friction resistance coefficient shows relatively minor fluctuations and remains nearly stable under different flow velocities. The shape resistance and friction resistance are determined by integrating pressure and shear forces over the AUV’s surface. At a flow velocity of
, the pressure distribution on the upper and lower sides of the AUV’s longitudinal section in a center plane at different instances is shown in
Figure 8. It is evident that due to the presence of the seafloor, the pressure variations in the lower surface of the AUV, especially in the bow and stern sections, are more pronounced.
Figure 9 presents the distribution of the skin friction coefficient on the AUV’s surface at different instances. Similarly, significant variations in shear forces can be observed in the bow and stern sections of the AUV, with minor fluctuations in the midsection. Overall, among the various hydrodynamic coefficients, the lift coefficient presents the most pronounced fluctuations.
When
, the variation in the hydrodynamic coefficients of the AUV at different distances from the seafloor is shown in
Figure 10. It can be observed that the coefficients are influenced by the underwater dune terrain, and the influence on the AUV diminishes as the distance between the AUV and the seafloor increases. When
, the fluctuations in the AUV’s hydrodynamic coefficients become negligible. However, concerning the friction resistance coefficient, significant fluctuations only occur when the AUV is positioned relatively close to the seafloor. This indicates that the instantaneous influence of turbulence variations on the AUV’s friction resistance is minimal.
To analyze the characteristics of hydrodynamic coefficient variations in turbulent flow fields, a Fourier analysis is performed on the time-domain variation curves of the AUV’s hydrodynamic coefficients for different incoming flow velocities. This analysis yields the amplitude–frequency variation curves of the hydrodynamic coefficients. The peaks are selected from these curves, and within a 2% bandwidth on either side of the peak frequency in the amplitude-frequency curve, a bandpass filter is applied to the original curves. This process results in the time-domain variation curves of hydrodynamic coefficients corresponding to the peak frequency.
When
, the Fourier analysis and filtering results of the time-domain hydrodynamic coefficient curves for different incoming flow velocities are shown in
Appendix A,
Figure A1,
Figure A2,
Figure A3,
Figure A4,
Figure A5,
Figure A6,
Figure A7,
Figure A8 and
Figure A9. It can be observed that higher amplitude is associated with high-frequency components when the flow velocity is relatively high. As shown in
Figure 11 and
Figure 12, within the turbulent region on the leeward side of the dune, a continuous process of vortex evolution and fragmentation occurs. When the flow velocity is high, the flow field possesses increased energy, leading to more intense vortex motion and promoting the fragmentation of smaller vortices. The dominance of high-frequency components in the flow field, along with the increased amplitudes of high-frequency phenomena, indicates the accelerated development of small vortices, enhancing the randomness of the flow field and resulting in pronounced variations in the AUV’s hydrodynamic coefficients. As the flow velocity decreases, the dominant components in the curves shift toward lower frequencies, accompanied by a reduction in the amplitude of high-frequency components. This shift implies a weakening in the phenomenon of vortex evolution and fragmentation, with large-scale vortices constituting the main components of the flow field while evolving at a slower pace. Furthermore, it is evident that with decreasing flow velocity, the dominance of low-frequency components is most pronounced in the resistance coefficient’s time-domain curve. However, for the lift coefficient and pitch moment coefficient time-domain curves, the frequency components dominating the behavior at low flow velocities are higher than those in the resistance coefficient curve. This indicates that the AUV’s lift and pitch moment present higher sensitivity to variations in the turbulent flow field, with the potential for significant changes still present at lower flow velocities.
When
, the Fourier analysis and filtering results of the time-domain hydrodynamic coefficient curves for different near-seafloor distances are presented in
Appendix A,
Figure A10,
Figure A11,
Figure A12,
Figure A13,
Figure A14,
Figure A15,
Figure A16,
Figure A17,
Figure A18,
Figure A19,
Figure A20 and
Figure A21. Within the range of
H/
D = 1.5 to 3.5, the hydrodynamic coefficient time-domain curves present larger amplitudes of high-frequency components. The vorticity distribution contours at different near-seafloor distances in the final time step are shown in
Figure 13. Due to the shear layer generated by the seafloor terrain, the flow field within this region is more turbulent. Moving away from this region, the intensity of vortex motion decreases, leading to a reduction in the frequency of flow field variations, and the dominance of low-frequency components in the hydrodynamic coefficient time-domain curves becomes evident. Furthermore, it is noteworthy that the dominant frequency component in the pitch moment coefficient time-domain curves is higher than the other two coefficients. This indicates that the AUV is prone to experiencing pitching motion in this turbulent flow field. As the AUV moves away from this region, the frequency and intensity of pitching motion will significantly decrease. However, during near-seafloor processes, the intense pitching motion could potentially pose collision risks.
Along the length of the AUV, the turbulent kinetic energy
k is calculated at 0.05 m from the upper and lower surfaces of the AUV in the longitudinal section of the AUV in the center plane. The distribution of turbulent kinetic energy near the AUV is shown in
Figure 14 and
Figure 15, where
is the longitudinal distance between the AUV surface and the AUV bow. It is evident that as the distance from the seafloor decreases, the turbulent kinetic energy near the AUV increases, which indicates that the fluid possesses greater energy and is more prone to forming vortex structures. Interestingly, it can be observed that when
H/
D = 2.5, the turbulent kinetic energy beneath the AUV is higher than when
H/
D = 1.5. However, such a phenomenon is not observed in the variation in turbulent kinetic energy above the AUV. Analyzing
Figure 13 reveals that this is because, at smaller near-seafloor distances, the presence of the AUV hampers the development of vortex structures between the AUV and the seafloor. To depict the vortex characteristics within the flow field more distinctly, the
Q-criterion method is used for identification.
Figure 16 displays the vortex structures corresponding to
Q = 10 in the flow field. For
H/
D = 1.5, the presence of the AUV limits the development of vortex structures beneath it, reducing their quantity. However, the AUV remains within the vortex structures, leading to continually changing forces exerted on the AUV. Moreover, the presence of the AUV affects the evolution of vortex structures. Notably, it can be observed that at smaller near-seafloor distances, the turbulent kinetic energy around the lower surface of the AUV gradually diminishes along the AUV’s longitudinal direction. This phenomenon arises because the bow of the AUV is located within a region with stronger vortex structures, which may result in vibration in practical applications.
Below is an analysis of the average characteristics of the AUV hydrodynamic changes. The average values of the AUV hydrodynamic coefficients under different incoming flow velocities and near-seafloor distances are listed in
Table 1. Higher flow velocities correspond to a reduction in the resistance coefficient value. As near-seafloor distance varies, there is no distinct pattern in the variation in the hydrodynamic coefficients. Overall, the total resistance coefficient presents an increasing trend with the increase in near-seafloor distance. This increase in the total resistance coefficient is primarily driven by the rise in the friction resistance coefficient.
Figure 17 shows the distribution of the average skin friction coefficients of the AUV for
at different near-seafloor distances. It is evident that with increasing near-seafloor distance, the average skin friction coefficient on the AUV surface gradually increases.
Figure 18 presents velocity distribution contours around the AUV. Influenced by the terrain, the leeward side of the dune presents lower flow velocities. As it moves farther away from the seafloor, the flow velocities increase, and consequently, the shear stress on the AUV surface increases, leading to an increase in friction resistance. However, it is observable that the average skin friction coefficient in the stern region of the AUV decreases with increasing near-seafloor distance.
Figure 19 shows the vortex structures in the flow field near the AUV at the final moment for
and
, with
Q = 30. In regions with higher flow velocities far from the seafloor, the shedding of stern vortices of the AUV becomes more obvious, leading to easier flow separation in the region near the stern, which results in a reduction in shear stress on the stern surface.
Regarding the lift coefficient, there is a general trend indicating a decreasing lift coefficient as the near-seafloor distance increases.
Figure 20 displays pressure distribution contours around the AUV. It is evident that as the near-seafloor distance increases, the pressure beneath the AUV decreases, leading to reduced pressure differences between the upper and lower surfaces and subsequently lowering the lift coefficient.
Figure 21 and
Figure 22 present comparisons among the average pressure distribution on the upper and lower sides in the longitudinal section of the AUV in the center plane at different incoming flow velocities for
and at different near-seafloor distances for
, respectively. It is evident that higher flow velocities correspond to greater average pressures on the AUV surface. The average pressure fluctuations are more pronounced in the bow and stern regions. Moreover, as the near-seafloor distance increases, the average surface pressure on the AUV decreases.
Figure 23 illustrates a comparison between the average pressures on the upper and lower sides in the longitudinal section of the AUV in the center plane for different near-seafloor distances when
. It is observable that as the near-seafloor distance increases, the average pressures near the bow and stern of the AUV become more similar.
4. Conclusions
AUVs play an increasingly significant role in marine exploration. However, existing assessments of AUV maneuverability and navigation design often neglect unsteady hydrodynamic disturbances caused by the seafloor. In this study, an analysis of the hydrodynamic performance of AUVs in turbulent flow fields generated by underwater dunes was conducted. The AUV was placed about 3 m from the crest of the dune. Using the LES method, the hydrodynamic characteristics of the AUV and flow field variations were investigated under different flow velocities and near-seafloor distances. The results of this study include the following. In turbulent flow fields, the hydrodynamic coefficients of the AUV present fluctuations within a certain range, which become more pronounced with increasing flow velocity. In the range studied in this paper, the amplitude of the curve fluctuation in the hydrodynamic coefficient can reach about 2–8 times its mean value. Among these coefficients, the variation in the pressure resistance coefficient predominantly affects the total resistance coefficient. The friction resistance coefficient of the AUV presents relatively minor fluctuations under different flow velocities and is less affected by turbulent flow fields. The lift coefficient and pitch moment coefficient are more sensitive to variations in the turbulent flow field, with higher flow velocities resulting in more pronounced changes. As the distance between the AUV and the seafloor increases, the fluctuations in the hydrodynamic coefficients gradually diminish, particularly for the resistance coefficient. Overall, when , the AUV moves away from the region of the flow field where turbulence is significant, and the influence of turbulence on the hydrodynamic performance of the AUV becomes negligible. Regarding the frictional drag, it remains relatively stable when . Additionally, when , the AUV hampers the formation of vortices below it.
In summary, the hydrodynamic performance of AUVs in turbulent flow fields caused by the underwater dune is influenced by the constantly changing flow field structure. This effect is particularly pronounced in high flow velocity conditions and when the AUV is situated closer to the seafloor. While this study provides an exploration of the hydrodynamic performance of AUVs in underwater dune terrain, further experimental validation and engineering applications are required. Future research can combine real-world scenarios to optimize AUV design and control strategies, adapting them to complex seafloor environments.