Numerical Investigation of the Resistance and Static Drift Condition of the Autosub Submarine

Abstract

Keywords: Autosub; Static Drift; Resistance; CFD; Hydrodynamic Coefficients; Submarine

1. Introduction

One of the factors that determine the design of submarines is their maneuvering performance. During the process of determining maneuvering performance, it is crucial to calculate the maneuvering coefficients that represent the hydrodynamic effects. Obtaining the hydrodynamic coefficients which are part of the equations of motion is one of the most important parts for the maneuvering calculations (Cardenas et al., 2019). Computational fluid dynamics, empirical, and experimental methods are used

to obtain the hydrodynamic characteristics of submarines. Hydrodynamic coefficients are usually obtained through experimental or numerical simulations. Experiments enable the direct determination of coefficients by making measurements, but due to the high cost and difficulty of experiments, numerical simulations are becoming increasingly popular. There are three main conditions at submarine’s motion; acceleration, cruise and rotating at constant angular velocity. These three conditions should be investigated in order to obtain the maneuvering characteristics. The hydrodynamic forces due to acceleration effects

*Corresponding author. *E-mail address: yarikan@yildiz.edu.tr Published by Yıldız Technical University Press, İstanbul, Türkiye This is an open access article under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

are calculated through planar motion mechanism (PMM) experiments. The hydrodynamic forces and moments which occur at cruise are determined by towing tank tests while the angular velocity effects are carried out by rotating arm experiments (Efremov et al., 2019). Ship model testing experiments have different methods of calculating the hydrodynamic coefficients. For each method, the calculation methods differ. PMM is a hydrodynamic test system which allows to impose static drift and dynamic oscillating motions to a surface ship or submarine model. On the other hand, the rotating arm test, which is a different test setup, is used to obtain coefficients while the model is rotating with a constant angular velocity. To measure straight motion values such as longitudinal and lateral forces, the towing tank test are conducted. Thus, coefficients for drag, pitch or yaw angle are measured. Since in towing tank tests linear movements are obtained, measurements related to angular velocity cannot be obtained. This is what separates PMM test from the rotating arm test. The use of these test setups have a very important place in obtaining the hydrodynamic coefficients needed while designing a submarine (Saeidinezhad et al., 2015). In this study, the Autosub underwater vehicle (AUV) is used which is a submarine developed by the British National Oceanography Centre. This submarine is commonly used by oceanographers for scientific research. The Autosub submarine is capable of staying underwater for extended periods of time and measures the physical, chemical, and biological properties of the underwater environment through various sensors. It is used for a variety of missions, such as exploring various geological features like underwater volcanoes, mountains, and canyons by measuring factors such as ocean temperature, salinity, and water quality. Additionally, it is used to examine and monitor underwater biological life. Furthermore, it is also used to investigate human-induced pollution and natural disasters, such as studying the effects of oil spills or tsunamis. Due to its ability to stay underwater for extended periods of time, the Autosub submarine has become an important tool in ocean sciences and has been used in numerous studies in this field. The Autosub submarine is also a good validation tool used for submarine maneuvering studies since there are comprehensive model test results shared in the open literature. Model tests for the Autosub submarine have been performed on a model scaled by the scaling factor of 1.346 by Kimber & Marshfield (1993) at the HASLAR facility (270 m × 12.2 m × 5.5 m deep). Further tests were performed by Fallows (2004) on a 2.5 m scale model of the Autosub submarine at the Solent University Towing Tank (60 m × 3.7 m × 1.8 m deep). Experimental results in the open literature for the Autosub submarine are presented for submarines of different scale. Resistance results are presented for the full scale submarine while the PMM and rotating arm results are presented in non-dimensional form by the use of the

scaled submarine model. The cruise speed of the Autosub is 2 m/s at full-scale. Kimber & Marshfield (1993) used in the scaled model a velocity magnitude of 2.69 m/s to obtain the same turbulence specification. Static drift tests are conducted at ±0 degree to ±10 degrees with an increment of 2 degrees (Kimber & Marshfield, 1993). Fallows (2004) in his PhD thesis shares a description of the experiments conducted in Southampton Institute Towing Tank. The full scale sea trials have been described in his study and experimental results have been shared (Fallows, 2004). Pioneering studies for experimental studies concerning UWV’s date back to the DARPA Suboff project where comprehensive model experiments are conducted. The DARPA Suboff Submarine is designed and recommended as a benchmark submarine model by Groves et al. (1989). The stability and control characteristics of the DARPA Suboff submarine model have been presented by Roddy (1990). There is a very large literature concerning the experimental and numerical investigation for the resistance prediction of underwater vehicles. Studies where the resistance of the generic forms like DARPA Suboff, BB2 Joubert, C-Scout are obtained experimentally (Crook, 1990; Roddy, 1990; Liu & Huang ,1998; Carrica et al., 2016; Thomas et al., 2003; Thomas et al., 2003; Mackay, M., 1988) and numerically (Bull, 1996; Anckermann, 2008; Fell, 2009; McDonald & Whitfield, 1996; Alin et al., 2010; Chase & Carrica, 2013; Carrica et al., 2019) can be mentioned as pioneering studies. The estimation of the maneuvering characteristics of an underwater vehicle is a challenging problem with various methods developed to solve this problem (Kırıkbaş et al., 2021a, 2021b). Literature concerning the numerical determination of the hydrodynamic derivatives for maneuvering models date back to Davidson &Ship (Davidson & Schiff, 1946). After Abkowitz (1964) who extended higher order terms for surface ships, Gertler& Hagen (1967) introduced the first model for submerged body. With the increase of computational power, computational fluid dynamics calculations have spread. Toxopeus & Vaz (2009) have carried out a study where the DARPA Suboff submarine model is used to investigate numerically the flow at different drift angles around the bare hull configuration. They used their own computational fluid dynamics code by implementing different turbulence models and conducted a verification and validation study (Toxopeus & Vaz, 2009). In another study Vaz et al. (2010) calculated the maneuvering forces and moments of the DARPA SUBOFF AFF-1 and AFF-8 configurations for 0° and 18° drift angles by using two viscous-flow solvers. The influence of different turbulence models namely, RANS (Reynolds-Averaged-Navier-Stokes) and DDES (Delayed-Detached-Eddy-Simulation) methods on the calculation of forces and moments were investigated (Vaz et al., 2010). Other studies where the static drift characteristics of the DARPA Suboff Submarine are investigated are Duman et al. (2018) where the static drift simulations of DARPA Suboff bare hull form have been carried out to

calculate the hydrodynamic forces and moment acting on the hull in the horizontal plane (Duman et al., 2021). Atik (2021) who investigated the suitable solution mesh and turbulence model for the DARPA SUBOFF submarine AFF-1 hull form by performing static drift test simulations (Atik, 2021). Kahramanoglu (2023) who has examined the scale effects on the horizontal maneuvering derivatives for three different scales for the fully appended DARPA Suboff submarine (Kahramanoglu, 2023). Maneuvering studies on the Autosub submarine using computational fluid dynamics calculations are as follows. By providing a comprehensive understanding of complex systems, Fallows (2004) outlined an approach to enhance the performance of UWV systems that are already in use. He used Taguchi experimental methods and made complementary sets of measurements in the laboratory on the full scale Autosub submarine. His study presented a method for developing a propulsion system for an AUV, such as the Autosub submarine. He presented about the generic attributes of these systems and their requirements. Wu et al. in their study aimed to reduce the total resistance of the Autosub submarine. For this purpose, simulations of microbubbles were carried out. When the bubbles passed close to the hull of the submarine, it caused a decrease in the density of the fluid and turbulence viscosity. It has been shown that a 50% improvement in the total resistance was achieved in submarines (Wu et al., 2006). In the study of Philips et al., the focus has been on evaluating the hull resistance of three different Autosub submarines, each designed with distinct shapes and sizes. The objective was to calculate the resistance experienced by these vehicles during their underwater missions. By utilizing CFD, the researchers were able to simulate the fluid flow around the Autosub submarine bodies and to accurately calculate the resistance values. The calculated resistance values were then compared with available experimental data obtained from physical tests and measurements. The results showed a favorable level of agreement between the calculated and experimental resistance values, indicating the reliability and accuracy of the CFD method (Phillips et al., 2007). Using steady-state computational fluid dynamics (CFD), Phillips et al. effectively replicated experiments which are known as rotating arm test and towing tank test to obtain steady-state hydrodynamic derivatives for a torpedo-style Autosub underwater vehicle (AUV). The predictions demonstrated excellent agreement in estimating sway forces, although there was a slight overestimation in induced drag and yaw moments. In addition, numerical methods accurately obtained the dynamic stability limits of the submarine, in close agreement with the experimental measurements (Phillips et al., 2010). In another study Phillips et al. calculated the resistance and hydrodynamic coefficients of the Autosub model, the CFD method used for steady-state conditions was used to successfully reproduce horizontal towing tank and rotating

arm experiments for a torpedo-style Autosub, and steadystate hydrodynamic derivatives were derived. While there was a very good match for the prediction of the sideways force, the induced resistance and yaw moment were found to be slightly higher than obtained. (Phillips et al., 2011). In the study of Joung et al. an Autosub concept design model was created and subjected to analysis using a commercial CFD program to evaluate its resistance characteristics. The CFD analysis provided measurements of pressure and velocity distribution around the submarine, as well as resistance measurements. Additionally, the analyses were expanded to investigate the effects of adjusting the sail and communication transducer positions, as well as the angle of attack of the propulsion nozzle, in order to optimize the Autosub’s design and minimize the resistance. The CFD results were validated by comparing the results with the ITTC 1957 correlation line. The study demonstrated that CFD can effectively estimate the total resistance of complex-shaped submarines. To expedite convergence, an automated mesh generation technique incorporating boundary layer inclusion was employed. Significant reductions in convergence time were achieved by examining object function and changing time of per iteration. It has been shown by sensitivity analysis that the angle of attack of the nozzle has a significant effect on the resistance value (Joung et al., 2012). Aslan in his master thesis investigated the hydrodynamic coefficients of the DARPA Suboff and the Autosub submarine by means of static drift and rotating arm calculations. CFD calculations were performed and a good agreement between numerical and experimental results was achieved (Aslan, 2013). Can in his master thesis calculated the static drag coefficients of the DARPA Suboff submarine and the Autosub underwater vehicle. In this research, the computational fluid dynamics (CFD) method was employed, and data regarding the static drift and rotating arm calculations were made. Steady and unsteady rotating arm calculations were performed. The obtained hydrodynamic coefficients values were compared with the results of the experiments presented in the open literature, and the maximum error rate was presented as 10% (Can, 2014). In this study the Autosub 3 geometry is used. The full-scale submarine has a length of 7 meter, a diameter of 0.9 meter and a speed range of 1 to 2 m/s. The aim of this study is to investigate the resistance and the static drift conditions of the Autosub submarine through CFD analysis. The yaw moments, sway forces and surge forces are investigated. Static drift conditions for different angles of attack are calculated for the scaled and resistance for different forward speed are obtained for the full-scale model of the Autosub. A mesh independency and a validation study has been done to determine an adequate mesh structure. This study has been done with the use of the computational fluid dynamics software Simcenter STAR-CCM+ which is a commercial software based on finite volume method to

calculate the transport of physical quantities on a discretized mesh. For modelling the fluid flow the Navier–Stokes equations are solved in each of the cells. The steady hydrodynamic analyses have been done at different drift angles by using the software. A mesh independency study has been done to determine the mesh structure that will be used in the analyses with 0,2,4,6,8 and 10 degrees of static drift angle. The case for 6 degrees drift angle has been selected for the mesh independency study. Five different mesh structure has been generated with different mesh element sizes. The result of these five analyses has been compared with the experimental results given in Phillips et al. (2007). As a result of this mesh independence study the mesh size that gives the results compatible with the experimental results has been selected. This selected mesh structure has been used while computing the other analyses.

Equation (2) displays the values of the three components of angular velocity (p, q, and r) when the sail is positioned horizontally on the bottom. (2)

Equation (3) provides the values of the three components of angular velocity (p, q, and r) when the sail is positioned vertically on the starboard side. (3)

3. Geometry Of Bodies

The Autosub autonomous submarine model has evolved from the past to the present with the advancement of technology. The National Oceanography Centre (NOC) in Wormley initiated a program to develop scientific applications for autonomous underwater vehicles. The Autosub submarine vehicle, which has multiple geometries tailored to different purposes, was designed according to its usage. The Autosub submarine has an approximate length of 7 meters and a diameter of 0.9 meters. The Autosub submarine model to be used in this study has a scale factor of 1.346. The geometric characteristics of the Autosub submarine model are provided in Table 1 (Can, 2014). The image of the created Autosub model can be seen in Figure 3 and Figure 4.

6. Degrees Static Drift Results

based on this angle. Table 2 presents the element count, results and deviations according to experimental results for different mesh densities. The analyses are conducted on a Windows operating system using a 4-core processor. The connection between the forces at 6 degrees of static drift and the mesh structure can be seen in Figure 7. Figure 8 shows the connection of the moments at 6 degrees of static drift with the mesh structure. Roache (1994) presented the Grid Convergence Index (GCI) method in his study. While there are many different methods, this method focuses on mesh refinement, which is one of the important areas in CFD studies. This method, which is presented to reduce the complexity in grid refinement studies, has been used in many different studies and

has been accepted by researchers. The mentioned method was edited by Celik et al. (2008) and presented again. In this study this edited method of GCI has been used as follows. Mesh size can be found by Equation (22). (22) N is the number of cells andVi is the volume of i th cell. Grid refinement factor can be found with Equation (23). h1, h2 and h3 is calculated with the help of Equation (22) for fine, medium and coarse grids, respectively. (23) After calculating the refinement factors between fine and medium; medium and coarse, we can calculate the apparent order which is p in Equation (24). (24)

ϕk is the solution of k th grid. That can be selected as a scalar value from a solution such as a sway force. ε21 and ε32 have been calculated with the help of the Equation (27) and these parameters used to calculation of s in Equation (26). The negative value of s means oscillatory convergence. The apparent order, p, has been calculated with the help of Equation (24) and (25). As can be seen in equation (24) there is a function related to p, which is q(p), in equation p. For this reason, an initial estimate was made while calculating p, and p was found iteratively.

(28) The convergence factor R can be obtained with the help of

Equation (28). (32) (29) in Equation (29) is extrapolated scalar value of selected

The Grid Convergence Index (GCI) can be found with Equation (32). Uncertainty analysis results are given in Table 3. When the data in Table 2 and Figures 7 and 8 are examined, it is seen that the error rate stabilized after Mesh 4. The number of cells, which directly affects the computational cost, increases approximately 1.9 times between Mesh 4 and Mesh 5. The solution time is significant in terms of computational cost, since the selected mesh will be used in the analyses which will be done in the next part of the study. Considering the capacity of the computer used, the change in the error rate was ignored and Mesh 4 was chosen.

5. Resistance Analyses

The full-scale geometry of the 7m length submarine is used in the resistance analyses. The mesh sizes used in the resistance analyses are the same as those obtained from the Mesh 4 mesh structure in the mesh independence study conducted for static drift analyses. The flow volume is recreated to be proportional to the full-scale size. As a result, there is an increase in the number of meshes. Four different analyses are conducted at speeds of 0.5, 1.0, 1.5, and 2.0 m/s. The results of these analyses can be seen in the Table 4 and Figure 9. The velocity distribution around the Autosub geometry can be seen in Figure 10. As can be seen in Table 4, the empirical results presented by Phillips et al. (2007) do not match with the test results performed by Fallows (2004). In the experiment conducted by Fallows (2004), the 2.5 m. length model was drawn from the water surface at a depth of 2.6 diameter. This means that the submarine is close to the water surface and produces waves (Phillips et al., 2009). In addition, a model

Figure 9. Comparisons of resistance predictions for Autosub (Phillips et al., 2007).

Figure 11. Variation of Sway Force (Y’) with Sway Velocity (v’).

Figure 12. Variation of Yaw Moment (N’) with Sway Velocity (v’).

with a length of 2.5 meters was used in the experiment. As the speed increases, the increase in the margin of error supports that the factor causing this difference is the wave resistance. In the thesis published by Fallows, these problems related to the test setup were mentioned. Another cause of error is the presence of a large mounting post on the test setup. The forces caused by this structure affected the test results. These reasons are the causes for the difference between experimental results (Fallows, 2004), CFD results and empirical results. On the other hand, the CFD result for 2m/s agrees with the experimental results from Kimber&Marshfield (1993) with an error rate of %10. Also, the CFD results have error rates less than %6 with the empirical results (Phillips et al., 2007). In addition to these the results match with the CFX solution made by Phillips et al. (2007) with an error rate of less than %2,6.

6. Static Drift Analyses

Six further analyses are performed for the static drift condition at angles of 0, 2, 4, 6, 8, and 10 degrees, with a velocity of 2.69 m/s. The obtained results are compared with the experimental data from Kimber&Marshfield (1993). Static drift results are presented in Table 5. The hydrodynamic sway force Y’ and yaw moment N’ are presented in Figure 11 and 12. Figures 13, 14, 15, and 16 show the results obtained from the CFD analysis. The highest and lowest values ​​in the obtained results differ by changing the static drift angle. However, to provide a comparative result, the velocity and pressure range are limited to a single value for each figure. Figure 13 shows the flow field around the submarine. It is seen that the characteristic of the flow around the submarine changes as the static drift angle increases.

Surfaces with a Q-Criteria value equal to 5 were obtained. The velocity distribution on these surfaces is shown in Figure 14. The Q-Criteria value allows us to examine the wake behind the submarine. As can be seen, as the angle increases, the maximum velocity obtained increase, and the angle of the wake and length of the wake also increases. Figure 15 shows the streamline drawn from the submarine surfaces. When the submarine is subjected to a static drift angle, a rotational flow is observed around it. As this angle increases, it is seen in the figures that the streamlines in the rear part of the submarine are more complex and have higher velocity. Figure 14. Q Criteria = 5 Surfaces Around the Submarine.

Figure 16 shows the fins in the aft body of ​​the submarine. The pressure distribution over these fins changes as the angle changes. As the angle increases, the region of

Figure 17. Vector Field Around the Submarine. maximum pressure on the fin is displaced. This causes an increase in the force created by the fins as the angle increases. This effect is one of the reasons why the yaw moment increases as the angle increases. The vector field around the submarine is shown in Figure 17. In this image given for the 10-degree static drift condition, the angle of the flow acting on the submarine is clearly seen. The resulting sway force and yaw moment are caused by the flow of the body acting at a certain angle. It is seen that it reaches 3.3 m/s in the cross section of this image performed at a speed of 2.69 m/s. These velocity zones affect the pressure zones around the submarine, causing sway force and yaw moment to occur. When comparing the force and moment values obtained through CFD with experimental results, it is observed that the error rates vary between -5% and 10% (Table 5). The results (Figure 11 and Figure 12) presented show that the sway forces and yaw moments obtained from the analyze give independent results from the mesh structure and are in consistency with the experimental results presented in the literature. As a result, an analysis method that can be used in future studies has been presented.

7. Conclusions

This study involves the force and moment calculations of the Autosub submarine using model and full-scale geometries. The RANS equations and two-equation turbulence models are employed in the calculations. Static drift analyses are conducted for angles of 0, 2, 4, 6, 8, and 10 degrees. The calculations are performed at a cruising speed of 2.69 m/s using a scale factor of 1.346. To determine the optimum mesh structure, a mesh independence study is carried out at 6 degrees static drift angle. The error rates of the experimental results and the calculated values in the analysis are used in the mesh independence study. After determining the optimum mesh structure with the help of the

uncertainty analyses and the mesh independence study, the analyses are completed for other angles and compared with the experimental results. Full-scale resistance analyses are conducted using the same mesh sizes. Resistance analyses are performed for the 7m full-scale geometry at velocities of 0.5, 1.0, 1.5, and

Data Availability Statement

The published publication includes all graphics and data collected or developed during the study.

Conflict Of Interest

The author declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Ethics

There are no ethical issues with the publication of this manuscript.

Financial Disclosure

The authors declared that this study has received no financial support.

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