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As part of a multi-nation study regarding CFD validation, conducted by the Submarine Hydrodynamics Working Group, viscous-flow calculations on the unappended hull-form of the DARPA SUBOFF sailing straight ahead and at oblique motion were conducted in order to verify the accuracy of the predictions. The study shows good general agreement with the experiments for local field values as well as for global quantities.

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... Table 1. Main dimensions of the AUV compared to the DARPA Suboff [11] Dimension ...

... Symbol AUV (λ = 1.588) DARPA Suboff [11] Length Aiming to study low noise propellers for underwater vehicles, a seven-bladed propeller was developed [1] applying Lifting Line Theory (LLT) [2] and Lifting Surface Theory (LST) [3]. The design was based on a CFD-calculated wake of the DARPA Suboff hull. ...

... AUV hull based on DARPA SUBOFF geometry[11] ...

In a joint project of the Brazilian Navy (CTMSP) and the Institute for Technological Research (IPT), the propeller of a DARPA Suboff based AUV was designed applying lifting line theory and manufactured. This paper presents the comparison of propeller tip vortex properties obtained on cavitation tunnel tests and numerical simulations, both in open water conditions. It represents an important issue in terms of propeller efficiency and acoustic investigation. The experiments were carried out at IPT’s facilities, in where thrust and torque were measured and the velocity field was registered using Particle Image Velocimetry (PIV), in order to obtain the vortex distribution pattern. The numerical approach consisted of simulating the propeller using RANS $k-\omega \, SST$ turbulence model in ANSYS ® CFX and StarCCM+ ® finite-volume software. These simulations were performed separately by CTMSP-team and IPT-team, respectively. Numerical methods were capable of estimate the total loads and vorticity values on the tip vortex regions, however there are limitations in reproduce the vortex geometry as measured by the PIV apparatus.

... In recent years, the use of CFD method on predicting maneuvering performance of underwater vehicles and submarines has become a very popular research field. Toxopeus [10] [18] have also studied selfpropulsion characteristics of DARPA Suboff bare hull form both modelling original propeller and actuator disc theory based on body force method. The differences of two approach have been presented. ...

... In addition to the experiments, numerical results have also been compared with those of another numerical study [10]. The subindex "MNT" (see Tables 5-7) stand for the Menter's one-equation turbulence model as explained in Toxopeus (2008). ...

... In addition to the experiments, numerical results have also been compared with those of another numerical study [10]. The subindex "MNT" (see Tables 5-7) stand for the Menter's one-equation turbulence model as explained in Toxopeus (2008). The presented results are in a good agreement with both experimental and the numerical results (Tables 5-7). ...

In this study, the effects of propeller on maneuvering forces of a submerged body have been investigated by implementing body force method. The flow around a submerged body has been solved using a commercial RANS (Reynolds-averaged Navier-Stokes) solver based on finite volume method (FVM). For this purpose, a benchmark DARPA-Suboff bare hull form (AFF-1) has been chosen for the calculations. Oblique towing analyses have been carried out for two different drift angles at two different Reynolds number with and without propeller effects. The propeller-hull interaction has been modelled with an actuator disc coupled with experimental open water data based on body force method at self-propulsion points. Verification study has been carried out using Grid Convergence Index (GCI) method to determine the optimum grid number. Validation study has been done in terms of maneuvering forces and moment acting on the gravity center of submerged body with the available experimental data. The results have also been compared with those of other numerical results.

... In recent years, the use of CFD method on predicting maneuvering performance of underwater vehicles and submarines has become a very popular research field. Toxopeus [10] [18] have also studied selfpropulsion characteristics of DARPA Suboff bare hull form both modelling original propeller and actuator disc theory based on body force method. The differences of two approach have been presented. ...

... In addition to the experiments, numerical results have also been compared with those of another numerical study [10]. The subindex "MNT" (see Tables 5-7) stand for the Menter's one-equation turbulence model as explained in Toxopeus (2008). ...

... In addition to the experiments, numerical results have also been compared with those of another numerical study [10]. The subindex "MNT" (see Tables 5-7) stand for the Menter's one-equation turbulence model as explained in Toxopeus (2008). The presented results are in a good agreement with both experimental and the numerical results (Tables 5-7). ...

In this study, the effects of propeller on maneuvering forces of a submerged body have been investigated by implementing body force method. The flow around a submerged body has been solved using a commercial RANS (Reynolds-averaged Navier-Stokes) solver based on finite volume method (FVM). For this purpose, a benchmark DARPA-Suboff bare hull form (AFF-1) has been chosen for the calculations. Oblique towing analyses have been carried out for two different drift angles at two different Reynolds number with and without propeller effects. The propeller-hull interaction has been modelled with an actuator disc coupled with experimental open water data based on body force method at self-propulsion points. Verification study has been carried out using Grid Convergence Index (GCI) method to determine the optimum grid number. Validation study has been done in terms of maneuvering forces and moment acting on the gravity center of submerged body with the available experimental data. The results have also been compared with those of other numerical results.

... This test case is similar to the previous one, except for the angle of attack; it is set equal to 18 o , increasing the complexity of the flow [26,27]. Figures 9 and 10 illustrate the streamwise velocity and kinematic viscosity contours, respectively, at the midplane of the hull, indicating qualitatively the capability of Galatea-I for such simulations. ...

... Figures 9 and 10 illustrate the streamwise velocity and kinematic viscosity contours, respectively, at the midplane of the hull, indicating qualitatively the capability of Galatea-I for such simulations. In Figures 11 and 12 the distribution of obtained pressure coefficients at leeward and windward side, respectively, of the hull (midplane) are presented and compared with the corresponding results of Gross et al. [26] and Toxopeus [27]. As one can observe, the distributions compare close especially at the front compartment of the submarine. ...

... As one can observe, the distributions compare close especially at the front compartment of the submarine. A difference among the compared results exists though at the rear end of the hull, where a thick turbulent boundary layer is observed; nevertheless, the current distribution appears to be among the reference ones [26,27]. ...

In this study an academic CFD code, named Galatea-I, is presented, capable for simulating inviscid, viscous laminar and viscous turbulent incompressible fluid flows. It employs the RANS (Reynolds-Averaged Navier-Stokes) approach along with the SST (Shear Stress Transport) turbulence model to predict turbulent flow phenomena, such as recirculations and separations of flow, on three-dimensional unstructured hybrid grids, composed of prismatic, tetrahedral and pyramidal elements. Discretization of the governing equations is obtained with a node-centered finite-volume scheme. Parallel processing and agglomeration multigrid scheme are implemented for the acceleration of the numerical process. As the title of this paper reveals, the solver is validated against the test cases of the DARPA SUBOFF program; in particular, flows over the SUBOFF bare hull submarine geometry at two incident angles and the SUBOFF hull with fairwater configuration are examined. The obtained results, compared to available in open literature experimental data as well as results computed by reference solvers, indicate the proposed methodology’s potential to accurately simulate complex fluid flows.
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... Bull et al. [2] validated computational prediction for nominal wake on generic submarine body. Toxopeus [3][4][5] carried out viscous flow calculations on bare hull SUBOFF for the longitudinal and circumferential pressure distribution at various drift angles and also during steady turn. Vaz et al. [6] calculated manoeuvring forces on submarine using two viscous solvers for a range of inflow angles: 0° to 18° and observed that due to larger inflow angles, vortices shed from the sail and hull are pulled down into the low pressure area at leeward side of and enter into propeller plane. ...

... A similar trend is observed for appended hull at zero incidence, except that the relatively high pressure at x = 0.2L and 0.9L due to presence of sail and control surface, respectively. Few additional tests are exclusively carried out for validation of test results with the published data [1,[3][4][5][6]. The tests with α = 0° to 40° (Figs. 10 and 11) indicated that the local minima of C P value occurs at x = 0.03L on the leeward side ranging from − 0.15 to − 0.65 for bare hull and − 0.15 to − 1.0 for appended hull. ...

To investigate the surface pressure distribution at high angles of incidence over a generic submarine hull form (SUBOFF), model tests were carried out for pressure measurements in the Wind Tunnel Facility at Naval Science & Technological Laboratory, India. Pressure measurements were performed for a range of high angles of incidence in angle of attack (± 40°) and drift (0 to 40°) on 1.372 m model at Reynolds number 1.7 × 10 6. The particulars of the SUBOFF model, test apparatus, measurement system, test results and observations are presented in the paper. The pressure measurement data generated from the above studies will complement the computational and experimental research on turbulent flows over submerged bodies at wide range of angles of incidence. Keywords Pressure measurements · High angle of incidence · Pressure coefficient · Sting-mounted system List of symbols C p Pressure coefficient, [-] L/D Length to diameter ratio, [-] L Length of hull form, [m] L CB nose Longitudinal position of center of buoyancy from nose, [m] R n Reynolds number, V 0 L/ υ, [-] V 0 Velocity of vehicle (or) free stream velocity, [m/s]

... Bull et al. [2] validated computational prediction for nominal wake on generic submarine body. Toxopeus [3][4][5] carried out viscous flow calculations on bare hull SUBOFF for the longitudinal and circumferential pressure distribution at various drift angles and also during steady turn. Vaz et al. [6] calculated manoeuvring forces on submarine using two viscous solvers for a range of inflow angles: 0° to 18° and observed that due to larger inflow angles, vortices shed from the sail and hull are pulled down into the low pressure area at leeward side of and enter into propeller plane. ...

... A similar trend is observed for appended hull at zero incidence, except that the relatively high pressure at x = 0.2L and 0.9L due to presence of sail and control surface, respectively. Few additional tests are exclusively carried out for validation of test results with the published data [1,[3][4][5][6]. The tests with α = 0° to 40° (Figs. 10 and 11) indicated that the local minima of C P value occurs at x = 0.03L on the leeward side ranging from − 0.15 to − 0.65 for bare hull and − 0.15 to − 1.0 for appended hull. ...

To investigate the surface pressure distribution at high angles of incidence over a generic submarine hull form (SUBOFF), model tests were carried out for pressure measurements in the Wind Tunnel Facility at Naval Science & Technological Laboratory, India. Pressure measurements were performed for a range of high angles of incidence in angle of attack (± 40°) and drift (0 to 40°) on 1.372 m model at Reynolds number 1.7 × 106. The particulars of the SUBOFF model, test apparatus, measurement system, test results and observations are presented in the paper. The pressure measurement data generated from the above studies will complement the computational and experimental research on turbulent flows over submerged bodies at wide range of angles of incidence.

... Basic dimensions of DARPA UV model are tabulated in Table 1 (Toxopeus, 2008). The form of the DARPA UV is presented in Figure 5. Then these forms presented in Figure 6 are re-scaled having the same displacement with the DARPA UV model as ∇=0.708 m 3 . ...

... Validation study is carried out using the benchmark DARPA UV model, presented in literature (Toxopeus, 2008) Table 2. The flow simulations around the DARPA UV are done in the next portions of the study using the same CFD methodologies and models as the flow simulations around the DARPA UV. ...

The nature inspired design perspective has been gaining popularity among researchers for various engineering fields, in recent years. One of this fields is underwater vehicles (UVs), which are widely used in many areas such as research, military and commercial applications. In this paper, resistance predictions of DARPA UV is validated with experimental results from the literature, at first. Then different UV forms are designed by inspiring boxfish geometry and the resistance characteristics of these UV forms were investigated by Computational Fluid Dynamics (CFD) analysis wtih the same conditions of DARPA UV. The numerical analyses were carried out considering that the flow is steady and incompressible, and RANS equations were modelled with k-Ɛ turbulence model. Total resistance predictions of boxfish inspired UV forms are carried out a wide range of velocity conditions. In the study, a brief literature review for boxfish inspired design of multifunctional structures are also briefly addressed. This study may be a case in point of new UV forms to be designed, inspired by marine animals or fish species in the future.

... CFD analysis carried out modeling the flow around the DARPA Suboff Submarine. Main particulars of DARPA Suboff submarine used in this work are presented in Table 1 (Toxopeus, 2008). (2011) and it extends for 3L in front of the submarine, 9L behind the submarine, and 4L to the side and 4L to the under the submarine. ...

... have performed experimental works for the DARPA Submarine model in David Taylor Research Center.Toxopeus (2008) performed viscous-flow calculations for bare hull of the submarine andGross et al. (2011) predicted the resistance of DARPA submarine model with different angle of attack values using CFD and compared these results with the towing tank test results. Chase (2012) performed self-propulsion simulations on the submarine hull with the INSEAN ...

Nature offers unlimited potential in addition to being a home for people for millions of years, and people have developed a wide variety of technologies for themselves using the potential that the nature has bestowed. In this study, the resistance characteristics of a submarine form which inspired by nature, were investigated by Computational Fluid Dynamics (CFD) approach for various velocity conditions. Firstly, CFD analysis of benchmark DARPA Suboff Submarine are carried out for different velocity conditions. In the computational analysis, the turbulent flow around the submarine is modeled with Reynolds Averaged Navier-Stokes (RANS) model with k-Ɛ turbulence model to solve the governing equations. The validation of the CFD approaches applied was provided by comparing the numerical results with the experimental results obtained from the literature, and verified by performing an uncertainty analysis based on the grid density in the computational domain. Then, a submarine hull form with the same length and average width that of the DARPA Submarine is generated by using the geometry of the shark form as source of inspiration. Resistance values of the nature inspired submarine are predicted by using the DARPA Submarine CFD approach and the results are compared with the results of the DARPA Submarine for the same hydrodynamic conditions. For the same length and average width; the resistance of the shark inspired submarine is achieved slightly higher than that of the DARPA Submarine. This study is expected to be an example for the study of new submarines that will be developed inspired by nature, especially by the forms of various marine animals.

... Together with the low demand of computational resources and ease of implementation of the problem setup to the CFD environment, working on linear damping coefficients became the initial area of research. Toxopeus [19] investigated the local field variables as well as global measures of the flow around a non-appended submarine hull at incidence. ...

A simulation approach relying on a single grid topology has been employed to replicate the motion characteristics of different experimental facilities, including towing tank, rotating arm mechanism, and planar motion mechanism using a single mesh. The control volume and computational mesh setup was built in a way to enable to perform both steady and time dependent simulations to compute entire set of coefficients required by the standard submarine equations of motion. Mesh is consisted of a rectangular prism shaped background and a spherical overset domain which can be rotated, circulated and oscillated depending on the simulation type. To enable the implementation of this approach to the rotating arm simulations, modifications to source code of the open-source computational fluid dynamics software OpenFOAM have been made. Motivation is to change the perspective on the problem by using the knowledge of mathematics behind the solution algorithms and the software structure. In this study extensive set of time-independent coefficients obtained via straight and oblique towing as well as steady rotation simulations are presented for a fully appended generic submarine geometry. Results are then compared with the benchmark experimental data. It is found that the consistency between results are quite satisfactory.

... With increasing improvement of computing efficiency, it is feasible to study the hydrodynamic performances of submarines based on viscous flow theory (Toxopeus, 2008;Chase, 2012;. CFD (Computational Fluid Dynamic) technology provides a fast and accurate method for studying the hydrodynamic proficiency of submarines in vicinity to broad open surface, demonstrating an increasingly important position and role (Ling et al., 2023;Cao et al., 2023). ...

In this study, the SUBOFF submarine is numerically modelled in order to investigate the hydrodynamic features and effects of submerged navigation near the free surface. At various speeds and depths below the surface, the hydrodynamic behaviors of the SUBOFF submarine are examined. From the CFD results, we can deduce that submergence depth significantly affects total resistance of SUBOFF navigation nearby free surface. Because the Kelvin wake of SUBOFF creates wave-making resistance when approaching the open surface head-on, the fraction of pressure difference resistance becomes dramatically with an increase in Fr. The principle of superposition of the divergent wave system and the transverse wave system gradually reveals the divergent wave system as Fr grows larger. The wave making energy is greater, and the submarine needs more power to overcome the wave making resistance.

... Time-averaged surface pressures and predicted forces and moments around the midbody agreed well with experimental measurements. Toxopeus (2008) conducted RANS to study the bare hull DRAPA SUBOFF sailing straight ahead and in oblique motion. Menter's one-equation turbulence model and twoequation SST k − ω model were used. ...

In this paper, we present an overview of numerical simulation methods for the flow around typical underwater vehicles at high Reynolds numbers, which highlights the dominant flow structures in different regions of interest. This overview covers the forebody, midbody, stern, wake region, and appendages and summarizes flow phenomena, including laminar-to-turbulent transition, turbulent boundary layers, flow under the influence of curvatures, wake interactions, and all associated complex vortex structures. Furthermore, the current issues and challenges of capturing these flow structures are addressed. This overview provides a deep insight into the use of numerical simulation methods, including the Reynolds-averaged Navier–Stokes (RANS) method, large eddy simulation (LES) method, and the hybrid RANS/LES method, and evaluates their applicability in capturing detailed flow features.

... Other reasons include a strong background regarding the nature of the oblique flows and cross-flow separation, as well as low demand for computational resources due to the time-independent nature of the problem. (Toxopeus, 2008) can be counted among the contributors to this category. ...

Numerical simulations of underwater vehicles are performed utilizing mainly two approaches. Recently there is an increasing tendency of utilization of free running simulations due to the development in the computational capacity. This approach has also some drawbacks such as the high computational cost and the scaling difficulties of results. On the other hand, mimicking the captive motions of experimental facilities to calculate the manoeuvring coefficients are still promising and a valid approach. Due to the different geometric characteristics of the experimental facilities, this approach requires generating several computational meshes. In order to overcome this cumbersome problem, this study aims to utilize the same grid structure for mimicking the motions of all experimental facilities. Manoeuvring coefficients of fully appended DARPA Suboff (AFF-8) are calculated via this single grid. An overset mesh approach is adopted to ease the simulation cases where a mesh motion is required. Additionally, flexibility of source code modification of the open-source CFD software OpenFOAM is utilized for the calculation of rotary manoeuvring coefficients. Results are compared and validated with the experimental and other numerical results available in the literature.

... Other reasons include a strong background regarding the nature of the oblique flows and cross-flow separation, as well as low demand for computational resources due to the time-independent nature of the problem. (Toxopeus, 2008) can be counted among the contributors to this category. To address the problem of dynamic stability in both horizontal and vertical planes and calculate the stability indices Gv and Gh, rotary motion coefficients must be calculated along with the linear damping coefficients. ...

A numerical simulation strategy based on a single grid topology has been adopted to simulate the motion behavior of different experimental facilities such as towing tank, rotating arm mechanism and planar motion mechanism (PMM). Ease of source code modification of open-source CFD software OpenFOAM is exploited in some cases to implement this strategy. Simulation cases which dictate a time dependent mesh motion are performed via a spherical overset mesh region that encircle the vehicle (DARPA Suboff AFF-8). Turbulence is modeled via k-ω SST which is known to have a good performance with-these kinds of-separation flows under consideration. Validation of the computational mesh and simulation results are performed by comparison of thoroughly analyzed parameters (drag vs. speed) and the results of other numerical and experimental studies. Results are consistent and in parallel with the previously published results.

... Still, the details of the mesh refinements and good CFD practices are not shown, and it is difficult to determine if a similar mesh can be used to design the fine details of another AUV or submarine body. Toxopeus 7 uses the top-bottom and port-starboard symmetries in a 90 , 3D axial flow model with 1.8 Â 10 6 cells and obtains a drag at Re ¼ 14 Â 10 6 that differs from the experimental results of David Taylors Research Center (DTRC) by about 1%. The k À x shear stress transport (SST) and other RANS models are also used for comparisons. ...

Turbulent flow is fundamentally three-dimensional (3D), but two-dimensional (2D) axisymmetric computational fluid dynamics (CFD) models of axial viscous flow over streamlined axisymmetric bodies yield quick results that are approximate but very useful for preliminary studies. This is shown by comparing the results of 2D axisymmetric and 3D CFD (STAR-CCM+) models of axial flow over the Defense Advanced Research Project Agency submarine model known as the DARPA SUBOFF. The CFD community is always in search of methods to reduce the overall computational time – preferably by large factors. The detailed illustration using the much-studied DARPA SUBOFF shows that this 2D axisymmetric model, in addition to being fast by a factor of more than 300, yields results for the total drag, the wall shear stress and wall pressure coefficients, and the velocity profile within the boundary layer at various locations on the body that are very nearly the same as those obtained using 3D simulations. The difference between the 2D CFD drag at a Reynolds number of 35.35 million and experimental results is only +2.05%. Thus, the method is ideally suited for preliminary optimization studies. The model chosen for use in any application depends on the outputs of interest. The simplest and fastest model that yields results with sufficiently low errors is the most desirable one. The model should also be robust and work well for new applications. In the preliminary design stage, a large number of options should be tried and ranked. Sub-optimal designs are often used because of the lack of time to investigate more options. A large database allows the chief designer to choose an appropriate option after considering various trade-offs. It is shown that the 2D axisymmetric model is well suited for preliminary design and the ranking of options. The error in the total drag is low and the flow in the nose and tail regions is shown to be computed with low errors. High accuracy is obtained by stating and using a few guidelines for meshing. The level of rigor in the verification and validation of the results is high and is rarely seen in recent literature. This should inspire confidence among the CFD community to use this method to study flows over streamlined axisymmetric bodies and new applications.

... Divsalar K. [2] and Budak et al. [1] both showed the hydrodynamic performance of bare hull SUBOFF model and improved it by changing its shape. Gross et al. [3] and Toxopeus [9] studied the flow around the bare hull SUBOFF model. Karim et al. [6] studied the viscous drag around axisymmetric underwater body. ...

The primary goals of this study are to evaluate a DARPA-SUBOFF bare hull model's hydrodynamic performance and determine its hydrodynamic properties using the commercial CFD code STAR CCM+. Finite volume method based on viscous and incompressible steady Reynolds-averaged Navier-Stokes (RANS) equations is used to simulate the flow around the bare submarine model. To take the effect of turbulence in to consideration, Because of the low computing cost and pretty accurate anticipate results, the Shear Stress Transport (SST) k-ω turbulence model is chosen. Results are compared with available experimental/theoretical results from other researchers in order to validate the computational method. There are three main parts of this model, namely the nose, parallel middle body and tail. All the simulations are carried out at u = 1.5, 2.57, 3.05, 5.14 & 6.1 m/s. The results show that with the increase in speed of the model, the drag force also increases and due to the model being axisymmetric, there is negligible lift force

... Due to the very limited availability of experimental and simulation data for microbubble based drag reduction, the present numerical framework is only validated by simulating the nobubble water flow around the bare hull DARPA SUBOFF, for which the experimental data can be obtained. The main particulars of the DARPA SUBOFF used are specified in Table 1 [15][16]. Since the SUBOFF model has a symmetry plane, only a half of the hull is considered in the simulation. ...

This paper presents a mixture-model based computational fluid dynamics (CFD) simulation on the two-phase microbubble flow over the hull of a SUBOFF model, aimed at assessing the roles of air-injection-to-freestream velocity ratio and air volume fraction in microbubble resistance reduction. The numerical framework consists of the Reynolds-average Navier-Stokes (RANS) equations and the standard k ε − turbulence model with standard wall function treatment, which is validated, without microbubbles, by existing experimental data of the same SUBOFF model. The effect of velocity ratio is then investigated by comparing different types of the resistance reduction at various water speeds, and the effect of air volume fraction on the friction resistance reduction is also studied with various air injection velocities. This study confirms that both the velocity ratio and air volume fraction play important roles in the microbubble resistance reduction phenomenon.

... Dramatic changes in the Reynolds number will require different grid structures in simulations due to the wall y + to correctly represent the viscous flow. Additionally, some studies prefer to use different grids for different PMM tests in system-based approaches (Toxopeus, 2008). Despite Cao et al. (2016) argue that similar grid topologies can be used for different captive tests, this will be an additional calculation workload. ...

Maneuvering abilities of underwater vehicles are one of the primary concerns for navies and in the civil field they provide great flexibility in working in confined environments. Numerical simulations of the motions of these vessels may be conducted via system-based or direct CFD approaches. In this study, we focus on direct CFD simulations of the benchmark DARPA Suboff AFF8 Configuration. The paper starts by showing the submarine's lack of course-keeping stability using the C-index. After validation of the numerical approach by self-propulsion tests (and the determination of the propeller rotation rate to achieve the required velocity), the results of an extensive set of standard maneuvering tests are presented. Turning circle, pullout and zigzag tests confirm that the DARPA Suboff does not have course-keeping ability. The submarine leans to the starboard side at neutral rudder angle. The maneuvering indices are investigated with respect to changing rudder angle with turning circle tests. High residual yaw rates are found in both side turnings in the pullout tests and the zigzag tests show the submarine's inadequacy in making sharp turns. Numerical simulations reveal that the DARPA Suboff has high turning ability but no course-keeping ability.

... Still, the details of the mesh refinements and good CFD practices are not shown, and it is difficult to determine if a similar mesh can be used to design the fine details of another AUV or submarine body. Toxopeus 7 uses the top-bottom and port-starboard symmetries in a 90 , 3D axial flow model with 1.8 Â 10 6 cells and obtains a drag at Re ¼ 14 Â 10 6 that differs from the experimental results of David Taylors Research Center (DTRC) by about 1%. The k À x shear stress transport (SST) and other RANS models are also used for comparisons. ...

Two-dimensional (2D) axisymmetric simulation is an efficient and time-saving computational fluid dynamics (CFD) technique when the body is axisymmetric, and the flow is along the length of the body. In the present paper, this technique is used to investigate turbulent flow around the bare hull configuration of the Defense Advanced Research Project Agency submarine model. Verification and validation of the results are done at three levels. The values of the total resistance, the distribution of the wall shear stress and the pressure on the surface, and the velocity profiles at various distances from the nose are compared with results obtained by using three-dimensional (3D) simulations and experimental results from the literature. The uncertainty in CFD results due to meshing is reported using Richardson Extrapolation. It is shown that the errors are minor, and the savings in computer memory and computation time are tremendous using 2D axisymmetric simulations. Good CFD practices essential for 2D axisymmetric simulations are also presented in this article, which will be helpful for the CFD community to conduct numerical investigations on any other axisymmetric bare hull bodies, such as torpedoes, missiles, submarines, and autonomous underwater vehicles in the future. Finally, the components of drag, coefficient of pressure, and wall shear stress at the highest speed (9.26 m/s) are also obtained using 2D axisymmetric simulation, which has not been previously reported in any other literature. The level of rigor in the 2D axisymmetric simulation reported here is rarely seen in recent literature.

... As an ensemble-averaging method, RANS method is widely employed for the advantage of high computational efficiency. Toxopeus (2008) presented a systematic verification and validation study for a submarine model under the straight-ahead and oblique conditions, achieving a good agreement between the numerical results and the experimental data. Cao et al. (2016) investigated the numerical solution of the flow around a submarine model under the steady turning condition, indicating the sufficiently fine grids and advanced turbulence models would be useful to improve the prediction accuracy. ...

Considering the complex flow features of a submarine under the maneuvering condition and their close relationship with the maneuverability, a numerical study is performed for the flow around the submarine under the rudder deflection condition. Taking the submarine model DARPA SUBOFF as the study object, the rudder force test with a wide range of rudder angles is simulated based on the open source CFD platform OpenFOAM. Two numerical methods of Unsteady Reynolds-Averaged Navier-Stokes (URANS) method and Delayed Detached Eddy Simulation (DDES) method are employed. A systematic convergence study is performed to clarify the effect of grid spacing and time step on the numerical solution. The computed hydrodynamic forces are compared with the available experimental data, and the effectiveness of the adopted numerical methods is validated. Besides, the obtained rudder forces and rudder parameters are compared and discussed. Based on the obtained flow field details of vortex structures, velocity fields, streamline distribution, turbulence levels, and pressure distribution, the flow mechanisms of the deflected rudders are analyzed. Compared with URANS method, DDES method presents a better capability of capturing the flow field details around the submarine under the tight maneuvering condition, where remarkable flow separation is involved.

... Divsalar K. [2] and Budak et al. [1] both showed the hydrodynamic performance of bare hull SUBOFF model and improved it by changing its shape. Gross et al. [3] and Toxopeus [9] studied the flow around the bare hull SUBOFF model. Karim et al. [6] studied the viscous drag around axisymmetric underwater body. ...

The main objectives of this study are to investigate the hydrodynamic performance of a DARPA-SUBOFF bare hull model and calculate its hydrodynamic characteristics using a CFD-based commercial code STAR CCM+. Finite volume method based on viscous and incompressible steady Reynolds-averaged Navier-Stokes (RANS) equations is used to simulate the flow around the bare submarine model. To take the effect of turbulence in to consideration, Shear Stress Transport (SST) k-ω turbulence model is selected as it can predict results fairly accurate with minimal computational cost. To validate the computational method, the results are compared with the available experimental/theoretical results of other researchers. There are three main parts of this bare hull model, namely the main body, nose, and tail. All the simulations are carried out at u = 1.5, 2.57, 3.05, 5.14 & 6.1 ms-1. The results show that with the increase in speed of the model, the drag force also increases and due to the model being axisymmetric, there is negligible lift force.

... To advance submarine hydrodynamic knowledge and tools and to support upkeep or successor programmes, DMO and MARIN have conducted a wide variety of bi-lateral or collaborative studies using empirical tools, potential and viscous flow methods and experiments on generic submarine hulls such as the SUBOFF (Toxopeus 2008;Vaz et al. 2010;Toxopeus et al. 2012), Joubert/BB1 (Joubert 2006;Kerkvliet 2013;Toxopeus et al. 2014;Overpelt 2014) and BB2 (Overpelt et al. 2015;Carrica et al. 2016;Toxopeus et al. 2019), but also on the existing Walrus class submarines (Bettle et al. 2010). These studies have led to increased applicability and accuracy of the submarine hydrodynamics toolkit. ...

Traditionally, submarine hydrodynamic design has focussed mainly on requirements regarding operational range, powering performance and manoeuvring ability for deeply submerged conditions. To improve the effectiveness of the boat, attention is also paid to operating near or at the surface and fortunately, computational tools and experimental methods are available to analyse the performance of submarines at these conditions. To advance submarine hydrodynamics knowledge and tools, DMO and MARIN have conducted a wide variety of bi-lateral or collaborative studies using potential and viscous flow methods and experiments on several submarine hull forms. In this article, several examples are presented of the development and use of hydrodynamic tools available during the design and assessment process of future submarines. These examples range from experimental and numerical studies into at-surface and periscope-depth resistance and powering, periscope-depth manoeuvring, high-fidelity flow around the boat during straight flight and manoeuvring motions, wakes of surface-piercing masts, to depth keeping under waves. It is demonstrated how state-of-the-art studies help in advancing the knowledge on submarine hydrodynamics and improving the overall design of modern submarines.

... In order to advance submarine hydrodynamic knowledge and tools and to support upkeep or successor programmes, DMO and MARIN have conducted a wide variety of bi-lateral or collaborative studies using empirical tools, potential and viscous flow methods and experiments on generic submarine hulls such as the SUBOFF (Toxopeus 2008;Vaz et al. 2010;Toxopeus et al. 2012), Joubert/BB1 (Kerkvliet 2013;Toxopeus et al. 2014;Overpelt and Nienhuis 2014) and BB2 (Overpelt et al. 2015;Carrica et al. 2016;Toxopeus et al. 2019), but also on the existing Walrus class submarines (Bettle et al. 2010). These studies have led to increased applicability and accuracy of the submarine hydrodynamics toolkit. ...

... Fig. 3 shows the velocity variation from numerical analysis in the vertical direction at x/L = 1.7 in the rear of the hull for zero pitch angle at Fr = 0.30. The experimental data for this case is obtained from [15]. Skin friction coefficients along the upper meridian line of the model are shown in Fig. 4. The experimental data for this case is obtained from [16]. ...

Comprehension of the flow field around any moving object in the ocean is crucial for developing acoustic as well as non-acoustic techniques of detecting those objects. These objects generate different wake patterns behind them in the form of turbulent wakes and V-shaped Kelvin envelopes while they move submerged. These turbulent wakes create one of the crucial starting points for the detection techniques. This paper investigates the far-field turbulent wake characteristics of such moving objects in a stratified medium through computational fluid dynamics simulations using the Reynolds-averaged Navier-Stokes (RANS) solver with a suitable turbulence model that uses various Froude numbers and pitch angles. The geometry of a DARPA sub off the submarine bare hull with linear density stratification is considered for the analysis. The simulation results are verified by experimental data reported by another researcher. Keywords-Wake of submerged objects, turbulent wake, wake in density stratified medium, far wake characteristics

... Most of the studies on the DARPA Suboff model are only based on the axisymmetric hulls appended with pairs of rudders and stabilizer fins that are small compared to the length of the hull, [14,[34][35][36]. Captive model tests provide information on flow physics but have certain limitations imposed by the equipment that constrain its usefulness. ...

A thorough numerical introspection for assessing the particular issues of large flow separations around a submersible hull by using various turbulence models is described. The generic Defense Advanced Research Projects Agency (DARPA hereafter) Suboff hull is considered in the present study. Detailed descriptions of the mathematics behind the hybrid Shear Stress Transport (SST), Detached Eddy Simulation (DES) and the Improved Delayed Detached Eddy Simulation (IDDES) are given. The ISIS solver of the Fine TM /Marine package is used to solve the flow problems. An adaptive mesh refinement is employed for resolving the flow inside the areas hosting significant flow gradients. Two sets of computations are analyzed: one refers to the straight-ahead course, whereas the other is focused on the static drift motions. Four angles of incident flow and three different incoming flow velocities are proposed for clarifying the details of the flow separation. Extensive grid convergence tests are performed for both working regimes and for all the meshes used in the present investigation. Extended verification and validation (V&V hereafter) of the numerical approach is performed through extensive comparisons with the experimental data. Global hydro-dynamic performance of the hull as well as the local flow features are discussed in detail. The study is concluded by a series of final remarks aimed at providing useful information for further similar investigations.

... Straight line and oblique towing tests are trivially simulated by using this frame of reference, as also did by Toxopeus [10]. For the non-trivial case of rotating arm simulations, a solution with respect to body fixed reference frame requires each water particle experienced centrifugal and Coriolis forces due to the rotation of the coordinate system. ...

Maneuvering of submerged vehicles is an important topic, which has been thoroughly investigated since the middle of the last century. Numerical methods were developed and applied particularly in the second half of this period. Starting from the early attempts of combining potential flow techniques with the boundary layer theory, today even wall-resolved LES (Large Eddy Simulation) is possible for this type of geometries at significantly large Reynolds Numbers from the engineering perspective.
In this study, literature about numerical methods is summarized since the last similar study was done by Patel & Chen [1]. Considering the amount of material and number of subtopics to be discussed; only a brief summary is given. For each of the subtopics, only the most significant studies in literature are referred in order not to prolong this presentation. A special emphasis is given to the turbulence modelling section because most of the progress in literature has been made under this topic.
This study is organized as follows; a brief introduction section to address the most important advancements between the study of Patel & Chen [1] and the end of the last millennium when these flows began to transform engineering flows from academic ones. The rest of the presentation is divided into subtopics, which must be under consideration for any CFD (Computational Fluid Dynamics) analysis. These are namely;
⮚ Governing equations
⮚ Computational Domain & Frame of Reference
⮚ Grid Generation
⮚ Initial and Boundary Conditions
⮚ Turbulence Modelling
⮚ Verification & Validation
⮚ Advanced Turbulence Treatment

... In spite of its apparent simplicity, the estimation of the hydrodynamic performances of a submerged hull is hampered by the lack of an established methodology for an accurate simulation of the heterogeneous flow characteristics, which still seem to be incompletely understood. Toxopeus (2008), Pacuraru et al. (2011), Chase (2012), , and Amiri et al. (2018) reported solutions in various operational instances, either for unbounded flow cases in straight-ahead or in static or dynamic maneuvers, or for operations in the proximity of the free-surface. Comparisons with the available experimental data proved an overall satisfactory accuracy of the numerical methods employed. ...

A series of numerical studies on an underwater vehicle performances, aimed at enhancing the accuracy of CFD application solutions is presented. The appended DARPA (Defense Advanced Research Projects Agency) Suboff is considered for which the unsteady RANS solutions are computed with the finite volume ISIS-CFD solver. Closure to turbulence is achieved either with the shear stress transport (SST) or with the hybrid detached eddy simulation (DES) SST turbulence models. The computed hull resistance is compared to the experimental data to validate the numerical approach. For the grid convergence test, computations are performed on four grids. Four different time steps are considered for the time convergence study. Solutions for the E1619 propeller working in open water are presented and discussed. Propeller open water curves are obtained for a range of advance coefficients covering high to moderate low loads, and results are compared with available experimental data. A V&V study is performed as well. Self-propulsion computations for the hull fitted with sail, rudders and the E1619 propeller are conducted and the resulting performances are presented and discussed. Finally, the near free-surface operation is considered by making use of a volume of fluid (VOF) approach. Three immersions are proposed and the solutions are compared with the unbounded flow results to emphasize the loss in the propulsion performance. The final remarks concludes that the main contribution of the work is the benefit in quality of using adaptive mesh refinement along with the hybrid SST-DES instead of using the faster but less accurate URANS SST methods or more the expensive LES-based methods.

... For predicting the hull resistance of the UUV form to be designed, first the well-known examinations on DARPA Suboff model were investigated elaborately ([1], [9], [10]), and this model was analyzed through the commercial software STAR CCM+ (Simulation of Turbulent flow in Arbitrary Regions -Computational Continuum Mechanics, C++ based). Then the analysis results obtained were validated by the physical towing tank tests given in [11]. ...

Research vessels or small craft equipped for the specific purposes lead geological, geophysical and oceanographic research both at the coastal and offshore areas for constructing and surveying the engineering projects such as offshore structures, undersea pipelines, harbours, oil and natural gas extraction plants from resources etc., which require extensive labourship. However, this research method applied entails very high costs and can also include risks for occupational safety and property due to the harsh weather conditions at sea. In addition, high precision measurements cannot always function from the sea surface during such research projects above-mentioned. Thus, unmanned underwater vehicles (UUVs) have been designed and produced intensively in the last two decades. The aim of this study was to generate form design of a proper unmanned underwater surveying vehicle to be able to conduct research on the geological and geophysical structure of the sea bottom as well as oceanographic opinions. Therefore, computational fluid dynamics (CFD) analysis of the DARPA Suboff submarine model was created, and the validation of the results obtained in these analyses was provided with those of the experiments of this DARPA Suboff model performed by Liu and Huang [1]. After successful conformity of the simulations carried out using the commercial software STAR CCM+ (Simulation of Turbulent flow in Arbitrary Regions - Computational Continuum Mechanics, C++ based), the UUV forms were created by means of different way including biomimicry methodology. In this context, the models of a mature goose-beaked whale (ziphius cavirostris), a mature sperm whale (physeter macrocephalus) and two torpedo-shaped UUV models as well a hybrid model including parts of a whale and torpedo-forms with the same displacement were analysed, and the results obtained were discussed.

... The general form of the governing equations in non-inertial reference frame formulation has been provided by [17]. It has been widely used by many researchers such as [2,5,[18][19][20][21][22][23][24][25]. Using dynamic mesh technique in deriving HCs can be avoided by employing the non-inertial reference frame. ...

A synthetic method of dynamic test for identifying hydrodynamic coefficients (HCs) of an ocean vehicle has been
proposed. The methodology consists of simulating various planar motion mechanism (PMM) tests simultaneously
in a single numerical analysis. As a technical method, a stationary numerical domain has been used. Therefore,
non-inertial forms of the fluid flow governing equations have been solved for simulating sinusoidal tests in a
stationary numerical domain. Consequently, the quality of the grids has been preserved during the analyses. With
considering of the well-known underwater geometry of DARPA-SUBOFF, validation of the numerical simulation
results has been done with the computing of the pure sway and the pure yaw tests. The PMM maneuvers were
induced to the numerical analyses by using a user-defined function augmented to the solver. The current results
are in good agreement with the experimental ones reported in the literature. Based on the superposition rule
which can be used for combining dynamic tests, a synthetic test has been designed consisted of the pure sway and
the pure yaw tests. It has been developed to form more advanced synthetic tests consisted of the various PMM
tests as well. The test has the capability to use for deriving non-linear HCs as well as the liner ones. The efficiency
of the proposed method has been compared with the other methods, which shows it is comparable to the other
approaches.

... The towed model was tested for varying Reynolds numbers (towing speeds), at two different submersion depths, and with and without the application of SHSs on the midbody. A useful aspect of using the SUBOFF model is the relatively large database of resistance data previously reported, recently discussed by Crook (1990), Roddy (1990), Liu andHuang (1998), andToxopeus (2008). ...

In the present study, the drag-reducing effect of sprayed superhydrophobic surfaces (SHSs) is determined for two external turbulent boundary layer (TBL) flows. We infer the modification of skin friction created beneath TBLs using near-wall laser Doppler velocity measurements for a series of tailored SHSs. Measurements of the near-wall Reynolds stresses were used to infer reduction in skin friction between 8%and 36%in the channel flow. The best candidate SHS was then selected for application on a towed submersible body with a SUBOFF profile. The SHS was applied to roughly 60% of the model surface over the parallel midbody of the model. The measurements of the towed resistance showed an average decrease in the overall resistance from 2% to 12% depending on the speed and depth of the towed model, which suggests a SHS friction drag reduction of 4–24% with the application of the SHS on the model. The towed model results are consistent with the expected drag reduction inferred from the measurements of a near-zero pressure gradient TBL channel flow.
Introduction
Nature has provided a plethora of materials to be studied and mimicked for everyday applications (Jung & Bhushan 2010). One material pertinent for use in the marine environment is the lotus leaf, which is known for its self-cleansing properties and resistance to wetting (Neinhuis & Barthlott 1997). More specifically, lotus-inspired superhydrophobic surfaces (SHSs) have been biomimetically developed for skin friction reduction in various flow applications (Bhushan et al. 2009; Samaha et al. 2012). Being exhaustively studied in small-scale laminar flows (see Rothstein [2010] for a review of SHS drag reduction and slip on SHSs), advances in the design and fabrication of SHSs have permitted application of these materials in more naval-relevant flows. Previously, it has been shown that in laminar flow, SHSs can reduce drag (Watanabe et al. 1999; Ou et al. 2004; Ou & Rothstein 2005; Zhao et al. 2007; Daniello et al. 2009; Woolford et al. 2009), and in low–Reynolds number turbulent flows, SHS drag reduction has been observed using small-scale, structured surfaces and large air–water interfaces (Henoch et al. 2006; Daniello et al. 2009; Park et al. 2014). However, these surfaces, in higher turbulence flows, can be unstable or become wetted. If the SHS possesses roughness features with small scales compared with the viscous length scale of the flow, researchers have demonstrated SHS friction drag reduction for wall-bounded, high–Reynolds number turbulent flows (Zhao et al. 2007; Aljallis et al. 2013; Bidkar et al. 2014; Golovin et al. 2016; Ling et al. 2016b; Gose et al. 2018a).

... The non-inertial reference frame formulations of the governing equations in their general forms have been presented by [19] and they have been widely used by many researchers such as [2,9,[20][21][22][23][24][25][26][27]. Using dynamic mesh technique can be avoided by applying the non-inertial reference frame. ...

In this paper, an approach is proposed for the estimation of hydrodynamic coefficients variation as functions of Reynolds number. The variation of rotary damping linear hydrodynamic coefficients for off-design velocities is studied by simulating the rotating arm test and using computational fluid dynamics. Numerical results are validated by comparison with experimental ones reported in the literature for geometry of the well-known underwater vehicle of DARPA SUBOFF and a good agreement is observed. The numerical tool is employed to study the effects of Reynolds number on hydrodynamic coefficients. Numerical results are used for deriving proper functions that estimates hydrodynamic coefficients using truncated power series expansion along with least square method. It can be concluded that it is more appropriate to use fitted functions instead of constant values especially at low Reynolds numbers.

... The use of Computational Fluid Dynamics (CFD) has gained increasing favor in recent decades, during which time computing power and improvements in numerical algorithms have been improving significantly; Using CFD could straightforwardly construct a virtual towing tank or wind tunnel (Yang & Löhner, 2003;Toxopeus, 2008;Fedor, 2009;Gross et al., 2011). The commercial CFD code ANSYS had been used to investigate an autonomous underwater vehicle and has resulted in a propeller race deduction (Rattanasiri et al., 2015). ...

This paper investigates the influence
of the forebody of a projectile-shaped model without appendages and propulsion system in a submerged condition. The
commercial steady RANS code, ANSYS Fluent, was used to conduct the simulations,
and the forebody was varied based on the Hull Envelope equation. From the
results, the model with nf = 2.75 was
the optimum design according to the bow efficiency coefficient. However, the model
with a blunt form (nf = 1) produced the lowest drag because it had the least wet surface area. For models with high nf, a high accelerating flow led to a
low-pressure condition after the impact of the fluid on the fore end. This
soaring pressure difference caused a flow separation, and therefore the fullness of the forebody affected the fluid flow around the body: the alteration of pressure, the flow speed, and friction as the primary
component of resistance.

... Regarding the use of RANS calculation in the design of submarine, Toxopeus(2008) and Zeng and Zhu(2010) demonstrated that RANS-based simulation could be used to predict the hydrodynamics of the scaled DARPA SUBOFF submarine in forward and oblique motions at small drift angle. In addition, Pan et al.(2012) proposed an approach for simulating the small drift motion and the harmonic motion of the same submarine with full appendage using the unsteady RANS-based simulation and the dynamic mesh technique. ...

... The geometry equations of the full scale are presented by Grooves et al. (1989). The main dimensions are shown in the work of Toxopeus (2008) and are compared to the AUV in Tab. 1. The AUV hull is shown in Fig. 1. ...

This paper presents the processes of project, Computational Fluid Dynamics (CFD) simulation and manufacture of a propeller for an autonomous underwater vehicle (AUV). The AUV has a hull configuration geometrically similar to the DARPA SUBOFF model. The propeller project methodology uses the Liftiing Line Theory coupled with the Lifting Surface Theory in order to obtain a propeller with optimum efficiency. The analysis of the propeller operation uses CFD simulation to obtain the performance curves. Finally, the complex geometry manufacture is conducted in a CNC milling machine equipped with CAM software.

... In addition, a validation study has been made for DARPA Suboff AFF-8 in terms of non-dimensional pressure and skin friction coefficients at Reynolds number of 1.4 Â 10 7 . Both non-dimensional parameters have been compared with those of another numerical study (Yang and L€ ohner, 2003) and experimental study (Huang and Liu, 1994;Liu and Huang, 1998) (Toxopeus, 2008), available in the literature for V ¼ 3.34 m/s. These parameters have been calculated along the submarine surface. ...

In this study, the resistance and self-propulsion analyses of the benchmark DARPA Suboff with E1619 propeller
have been done using Computational Fluid Dynamics (CFD) method. Single phase analyses have been carried out
by assuming 3-D, turbulent, incompressible and steady ﬂow, thus the governing equations (RANS Equations) have
been discretized with ﬁnite volume method (FVM). First, veriﬁcation and validation studies have been carried out
in order to determine the optimum grid numbers for resistance analyses of bare and appended forms, and then for
open water propeller analyses. The numerical studies have been done by taking the propeller-hull interaction into
consideration by two methods for different velocities. First, the propeller has been modeled as an actuator disc
based on body force method coupled with the experimental open water data. The propeller itself has later been
modeled behind the hull with a rotating region. Performance analyses have been carried out at the self-propulsion
points determined by these two methods. Self-propulsion characteristics have been estimated using thrust identity
method. Finally, a comprehensive investigation of wake has been carried out by comparing the present results
with those of other studies and the applicability of CFD on self-propulsion prediction of the underwater vehicles has been discussed.

... Few open literature studies describe the flow about a conventional submarine. The studies using the DARPA SUBOFF model (Alin et al., 2010a;Widjaja et al., 2007;Alin et al., 2010b;Chase and Carrica, 2013;Toxopeus, 2008) for example are based on an axisymmetric hull with a cruciform rudder and a fin that is small compared to the length of the hull. Captive model tests provide information on flow physics but have certain limitations that constrain their usefulness. ...

This investigation discusses the flow physics of the fully appended DSTO generic submarine model at both straight ahead conditions and during a 10° side-slip. Reynolds Averaged Navier Stokes (RANS) and Large Eddy Simulation (LES) computations have been performed and are compared with model-scale experiments. The experiments have been carried out in the DSTO Low-Speed Wind Tunnel, with data collected using pressure probes, Particle Image Velocimetry (PIV) and flow visualization using wool-tuft streamers. Computational studies using LES on unstructured meshes of up to 340 million cells provide detailed surface and off-body flow field data, complementing the experimental investigations and providing the opportunity for reciprocal validation of experiments and computations. Surface-flow patterns for the DSTO generic submarine model at 10° yaw and a freestream Reynolds (Re) number, based on wind tunnel speed and hull length, of Re=4.5×106 were obtained. The cross-stream velocity for the DSTO generic submarine model at 10° yaw and Re=2.7×106 was measured using PIV. The in-plane velocity was measured at three streamwise locations corresponding to 65%, 84% and 98% of the submarine model length. LES computations were performed using an incompressible LES flow solver developed using OpenFOAM and unstructured tetrahedral grids generated utilizing a patch-based approach to facilitate high near-wall resolutions and arbitrary refinement for appendage wakes.

... Studies are reported for DARPA submarine, in bare hull and appended hull configuration, for which extensive experimental data is available 9-12, . Ref 13 gives an account of numerical estimation of bare hull DARPA submarine at incidence while 10 gives key techniques for better numerical prediction of forces and moments at incidence. Ref 9,11,12 gives detailed analysis of the integral values as well as flow parameters for DARPA submarine. ...

Present study consists the effect of variation of the vehicle length on the hydrodynamic forces and moments of axisymmetric underwater vehicles due to angle of attack. Five different vehicle lengths are used for this study (L/D varying between 10 and 15) by experimental, numerical and empirical methods. Experimental investigation is done in a tow tank using a VPMM. Numerical analysis is carried out using commercial CFD code Fluent 6.2. The empirical estimation is based on method suggested by Allen & Perkins. Results show that the linear coefficients vary linearly with L/D, while the nonlinear coefficients vary nonlinearly with L/D for the range tested.

There are several parameters in designing undersurface vessel forms, the most important of which is the hull's total strength, which includes the strength of the hull and its attachments. According to studies, 70 % of the total strength of the vessels is related to their hull only without attachments. The hull has three major parts: nose, cylinder, and heel. The advanced vessels' architecture has a parallel shape (cylinder shape). This cylindrical part is important in examining the used volume by pilots and vessel equipment. This paper uses the CFD method to examine the vessel's shape, and the resistive force and volumetric-aqueous efficiencies are extracted. An optimum profile is extracted by the values of resistive force and volumetric-aqueous efficiencies. The results indicate the significant effect of the hull form on the hydro-acoustic noise of the hull. In other words, by optimizing the hydrodynamic form of the hull, the noise propagation can be reduced as much as possible. Also, the linear slope of the optimized hull is not optimized more than the hull. This means that the turbulence caused by the optimized hull has a higher damping potential.

Trip-resolved large-eddy simulations of the DARPA SUBOFF are performed to investigate the development of turbulent boundary layers (TBLs) in model-scale studies. The primary consideration of the study is the extent to which the details of tripping affect statistics in large-eddy simulations of complex geometries, which are presently limited to moderate Reynolds number TBLs. Two trip wire configurations are considered, along with a simple numerical trip (wall-normal blowing), which serves as an exemplar of artificial computational tripping methods often used in practice. When the trip wire height exceeds the laminar boundary layer thickness, shedding from the trip wire initiates transition, and the near field is characterized by an elevation of the wall-normal Reynolds stress and a modification of the turbulence anisotropy and mean momentum balance. This trip wire also induces a large jump in the boundary layer thickness, which affects the way in which the TBL responds to the pressure gradients and streamwise curvature of the hull. The trip-induced turbulence decays along the edge of the TBL as a wake component that sits on top of the underlying TBL structure, which dictates the evolution of the momentum and displacement thicknesses. In contrast, for a trip wire height shorter than the laminar boundary layer thickness, transition is initiated at the reattachment point of the trip-induced recirculation bubble, and the artificial trip reasonably replicates the resolved trip wire behaviour relatively shortly downstream of the trip location. For each case, the inner layer collapses rapidly in terms of the mean profile, Reynolds stresses and mean momentum balance, which is followed by the collapse of the Reynolds stresses in coordinates normalized by the local momentum thickness, and finally against the 99% thickness. By this point, the lasting impact of the trip is the offset in boundary layer thickness due to the trip itself, which becomes a diminishing fraction of the total boundary layer thickness as the TBL grows. The importance of tripping the model appendages is also highlighted due to their lower Reynolds numbers and susceptibility to laminar separations.

The flow around an axisymmetric body of revolution (DARPA SUBOFF bare model) at Re = 1.2 × 107 is numerically investigated using the wall-modeled large eddy simulation (WMLES). To evaluate the capabilities of WMLES in such wall-bounded turbulent flows, the effects of the wall stress model and sampling distance are systematically studied. The numerical results of the non-equilibrium wall stress model with an appropriate sampling distance are in good agreement with the experiments in terms of pressure coefficient, skin-friction coefficient, and drag coefficient. On this basis, the thickening of the turbulent boundary layer and the expansion of the wake can be clearly observed through flow visualization, especially using the Liutex vortex identification method.

Submarines’ manoeuvrability both in intact and degraded operating conditions is the main design concern starting at the very early stages of design. This increased complexity of the design process compared to a surface vehicle can only be handled by using dynamics numerical simulations on both the vertical and horizontal manoeuvring planes. To this aim, a 6-DoF method is presented, validated, and applied to study the manoeuvring characteristics of several vessels. The analysis has been conducted considering two standpoints, i.e., to verify the design handling capabilities of the vehicles at low and high speeds and to study the off-design residual abilities in the eventual case of emergency operations with jammed/lost-control surfaces. The influence of different design features, such as, e.g., the stern plane “+” and “x” configurations, fairway size and positioning, hull dimensional ratios and restoring capabilities have been analysed in terms of impact on turning ability, course and depth changing abilities, and vertical/horizontal course stability, including the vertical damping ratio and critical velocity.

A new type of pump-jet propulsor (PJP) was designed and installed on the DARPA Suboff. The installation position of this new PJP is different from the traditional PJP, which gives more possibilities to improve the comprehensive performance of submarine. The duct of PJP has been automatically modeled based on pumped rotor, stator and hull shape. The rotor of PJP has been modeled as an actuator disc based on body force method coupled with the experimental open water data. The hydrodynamic performance analysis was applied on the self-propulsion point, and the self-propulsion characteristics were estimated by the thrust identity method. Moreover, the pressure and velocity distribution for different duct geometric parameters have been compared and discussed. The results indicate that the size of the duct has an impact on the generation of negative pressure zone and the wake distribution. When the geometric parameters of duct are equal to r = 0.75R, L = 3.5D and H = 0.8D, the overall performance is superior. The new pump jet destroys the circumferential correlation of the duct vortex and accelerates the dissipation of the vortex.

A numerical investigation about the effects of Reynolds number on the flow around an appended axisymmetric body of revolution - Volume 884 - Antonio Posa, Elias Balaras

The creation of a database of hydrodynamic loads for a generic submarine hull with a casing is proposed due to a lack of data in the open literature on the loading effects of submarine casings. This work presents a numerical methodology for the eventual creation of such a database. Steady-state Reynolds-averaged Navier–Stokes simulations were conducted for the Joubert BB2 generic submarine hull in translation, with and without a deck casing while deeply submerged, and with and without a casing in a wind tunnel. Simulation results at a Reynolds number of Re = 5.24 × 10⁶ provide hydrodynamic load increments due to the submarine deck casing, and are validated against unique experimental data for a range of angles of attack, −15°≤α≤15°, and angles of drift, −30°≤β≤30°. The estimated numerical error of the in-plane force and moment were 8.1% and 6.8%, respectively, and 2.2% and 3.7% for the out-of-plane force and moment, respectively. The simulation results were useful in evaluating the interference of the experimental support system and investigating the hydrodynamic loading effects of the casing. It was found that the addition of a casing can alter the in-plane hydrodynamic loads by at least 30%, and can also introduce out-of-plane loads of comparable magnitude.

This study is concerned with the turbulent shear flow around the DARPA SUBOFF body undergoing a turning maneuver at drift. Steady Reynolds-averaged Navier-Stokes (RANS) equations were solved in a rotating frame of reference down to viscous sub-layer using two different k-ω turbulence models. Grid-convergence of the numerical solutions was ascertained using three systematically refined grids with up to 19 mln elements. The Wilcox' k-ω model predictions closely reproduce the salient features of the flow such as the cross-flow separation, the streamwise vortices, and the resultant force and moment acting on the body. The change in the effective drift angle along the body in turning strengthens cross-flow on the aft body and augments side force. It still remains a challenge to accurately resolve the sail vortex over a long distance. The computations showed measurable effects of the sting on the force and moment.

Computational Fluid Dynamics (CFD) simulations using Reynolds Averaged Navier-Stokes (RANS) equations are increasingly adopted as an analysis tool to predict the hydrodynamic coefficients of underwater vehicles. These simulations have shown to offer both a high degree of accuracy comparable to experimental methods and a greatly reduced computational cost compared to Large Eddy Simulation (LES) and Direct Numerical Simulation (DNS). However, one of the major challenges faced with CFD simulations is that the results can vary greatly depending on the numerical model settings. This paper uses the DARPA SUBOFF hull form undergoing straight-line and rotating arm manoeuvres at different drift angles to analyse the hydrodynamic forces and moments on the vehicle against experimental data, showing that the selection of the boundary conditions and turbulence models, and the quality of the mesh model can have a considerable and independent effect on the computational results. Comparison between the Baseline Reynolds Stress Model (BSLRSM) and Shear Stress Transport with Curvature Correction (SSTCC) were carried out for both manoeuvres, showing that with a sufficiently fine mesh, appropriate mesh treatment, and simulation conditions matching the experiments; the BSLRSM predictions offer good agreement with experimental measurements, while the SSTCC predictions are agreeable with the longitudinal force but fall outside the experimental uncertainty for both the lateral force and yawing moment.

The flow around a body of revolution with an appendage controlled by electromagnetic force is calculated by a finite volume method in order to assess the influence of the appendage on the flow and the control effect of the electromagnetic force. The Reynolds number (Re) base on the hull length is 1.0 x 10(7). An electromagnetic actuator is flush-mounted on the surface of the appendage to generate streamwise eletromagnetic force (Lorentz force) for flow control. The flow around the body at straight course and 6A yaw controlled by Lorentz force is simulated and discussed. The results indicate that the elliptical appendage introduces a complex wake structure and force fluctuation. The wake of the appendage has less influence on the boundary layer of the body at 6A yaw than at straight course. When the Reynolds number is as high as 1.0 x 10(7), the flow field and dynamic characteristic of the body approximate to the Euler solution. The Lorentz force may suppress the near-wall separation from the appendage effectively and reduce the drag and vibration, especially in the straight course case.

The understanding of three-dimensional separation is lagging behind the understanding of two-dimensional separation due to its greater complexity and the small number of universal or canonical flow problems. Three-dimensional separation occurs, for example, when low aspect ratio devices such as submarines and torpedoes are operated at large angles of attack, . Two low aspect ratio geometries, the DARPA Suboff bare hull geometry and a hemisphere-cylinder geometry were investigated. Numerical simulations and water tunnel experiments for the DARPA Suboff bare hull geometry which is a prototypical submarine shape, show little flow separation at = 30deg and for Reynolds numbers based on diameter of Re = 10, 000 and Re = 20, 000. A hemisphere-cylinder geometry was derived by replacing the Suboff forebody with a hemisphere. Simulations and water tunnel experiments were carried out for Re = 2000 and 5000 and for = 10deg and 30deg. For = 10deg a large separation bubble that is shedding is observed on the leeward side. For = 30deg two counter-rotating leeward vortices appear and shedding is suppressed. Proper orthogonal decomposition and Fourier analysis in time are employed for investigating the unsteady fluid dynamics. Conclusions are drawn with respect to the mean flow topology and possibly relevant hydrodynamic instabilities. Copyright © 2012 by the authors. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.

This paper presents a study on the influence of the iterative error on the numerical uncertainty of the so-lution of the Reynolds-averaged Navier-Stokes equa-tions. Two main topics are addressed: the estimation of the iterative error; and the influence of the iterative error on the estimation of the discretization error. Iterative error estimators based on the L ∞ , L 1 and L 2 norms of the differences between iterations and on the normalized residuals are tested on three test cases: the 2-D turbulent flow over a hill, a 3-D flow over a finite plate and the flow around the KVLCC2M tanker at model scale Reynolds number. Two types of pro-cedures are considered, one using the data of the last iteration performed and the other using an extrapola-tion based on a least squares fit to a geometric pro-gression. In the latter case, the option of including the standard deviation of the fit in calculation of the error estimator is also tested. The results show that the most reliable estimates of the iterative error are obtained with the extrapolation technique including the effect of the standard devia-tion of the fit applied to the L ∞ norm of the differences between successive solutions. To obtain realistic es-timates of the iterative error one should avoid the use of the L 2 and L 1 norms and the use of the differences obtained in the last iteration. The results further suggest that the contributions of the iterative and discretization errors to the numerical uncertainty are not independent. Nevertheless, for the levels of grid refinement tested it is not necessary to converge a solution to machine accuracy to obtain a negligible contribution of the iterative error. It suf-fices to ensure that the convergence criterion guaran-tees an iterative error roughly 2 to 3 orders of magni-tude below the discretization error.

A formalism will be presented which allows transforming two-equation eddy viscosity turbulence models into one-equation models. The transformation is based on Bradshaw's assumption that the turbulent shear stress is proportional to the turbulent kinetic energy. This assumption is supported by experimental evidence for a large number of boundary layer flows and has led to improved predictions when incorporated into two-equation models of turbulence. Based on it, a new one-equation turbulence model will be derived from the k-epsilon model. The model will be tested against the one-equation model of Baldwin and Earth, which is also derived from the k-epsilon model (plus additional assumptions) and against its parent two-equation model. It will be shown that the assumptions involved in the derivation of the Baldwin-Barth model cause significant problems at the edge of a turbulent layer.

The near-field behavior of a wingtip vortex flow has been studied computationally and experimentally in an interactive fashion, The computational approach involved using the method of artificial compressibility to solve the three-dimensional, incompressible, Navier-Stokes equations with experimentally determined boundary conditions and a modified Baldwin-Barth turbulence model. Inaccuracies caused by the finite difference technique, grid resolution, and turbulence modeling have been explored. The complete geometry case was computed using 1.5 million grid points and compared with mean velocity measurements on the suction side of the wing and in the near wake. Good agreement between the computed and measured flowfields has been obtained. The velocity distribution in the vortex core compares to within 3% of the experiment.

A theoretical analysis of TNT interfaces was carried out. A new set of diffusion coefficients was derived that effectively resolves the freestream dependency. Computations for a flat-plate constant-pressure boundary layer and for a two-dimensional airfoil demonstrated the effective elimination of the freestream dependence at low freestream eddy-viscosity levels, while maintaining the correct near-wall solution.

Experimental measurements of the flow fields from an axi-symmetrical body with and without appendages were made in the Carderock Division, Naval Surface Warfare Center (CDNSWC) and Tracor Hydronautics Ship Model Basin (HSMB). These experimental data are intended to serve as the data base for the Computational Fluid Dynamics (CFD) validations and other submarine related flow field analyses and was identified as the Defense Advanced Research Projects Agency (DARPA) SUBOFF project. Previous reports have documented various aspects of this SUBOFF test program. This report summarizes all collected data set in tabulated formats and serves as the final database for future submarine flow research.

A program of straightline captive-model experiments was performed in the vertical and horizontal planes of motion at deep submergence was performed in the vertical and horizontal planes of motion at deep submergence to determine the stability and control characteristics of the DARPA SUBOFF model. The experiments were performed for the following configurations: (1) the model fully appended in the vertical plane of motion, (2) fully appended in the horizontal plane, (3) unappended hull, (4) hull plus sail, (5) hull plus control surfaces, (6) and hull plus ring wing (Number 1). The results of the experiments indicate that the model is unstable in all of the conditions investigated.

Two new two-equation eddy-viscosity turbulence models will be presented. They combine different elements of existing models that are considered superior to their alternatives. The first model, referred to as the baseline (BSL) model, utilizes the original k-omega model of Wilcox In the inner region of the boundary layer and switches to the standard k -epsilon model in the outer region and in free shear flows. It has a performance similar to the Wilcox model, but avoids that model's strong freestream sensitivity. The second model results from a modification to the definition of the eddy-viscosity in the BSL model, which accounts for the effect of the transport of the principal turbulent shear stress. The new model is called the shear-stress transport-model and leads to major improvements in the prediction of adverse pressure gradient flows.

Measurements of flows over an axisymmetric body with various appendages in a wind tunnel: the DARPA SUBOFF experimental program

- T Huang
- L Liu
- N Groves
- T Forlini
- J Blanton
- S Gowing

T. Huang, H.-L. Liu, N. Groves, T. Forlini, J. Blanton and S. Gowing, Measurements of flows over an axisymmetric body with various appendages in a wind tunnel: the DARPA SUBOFF experimental program, in: 19th Symposium on Naval Hydrodynamics, Seoul, South Korea, August 1992, pp. 312– 346.

Practical grid generation tools with applications to ship hydrody-namics

- L Eça
- M Hoekstra
- J Windt

L. Eça, M. Hoekstra and J. Windt, Practical grid generation tools with applications to ship hydrody-namics, in: 7th International Conference on Grid Generation and Computational Field Simulations, Hawaii, February 2002.

On the influence of grid topology on the accuracy of ship viscous flow calculations, in: 5th Osaka Colloquium on Advanced CFD Applications to Ship Flow and Hull Form Design

- L Eça
- M Hoekstra

L. Eça and M. Hoekstra, On the influence of grid topology on the accuracy of ship viscous flow
calculations, in: 5th Osaka Colloquium on Advanced CFD Applications to Ship Flow and Hull Form
Design, Lisbon, Portugal, March 2005, pp. 1–10.

An evaluation of verification procedures for CFD applications

- L Eça
- M Hoekstra

L. Eça and M. Hoekstra, An evaluation of verification procedures for CFD applications, in: 24th
Symposium on Naval Hydrodynamics, Fukuoka, Japan, July 2002.

Geometric characteristics of DARPA SUBOFF models (DTRC Model Nos

- N C Groves
- T T Huang
- M S Chang

N.C. Groves, T.T. Huang and M.S. Chang, Geometric characteristics of DARPA SUBOFF models
(DTRC Model Nos. 5470 and 5471), Report No. DTRC/SHD-1298-01, March 1998.