2D axisymmetric and 3D CFD simulations of flow over the benchmark DARPA SUBOFF submarine model

Hi everyone! My name is Rahul Krishna, and I am a researcher in the field of Computational Fluid Dynamics. Specifically, I work with underwater vehicles, including Autonomous Underwater Vehicles and Submarine models. Today, I am excited to give a talk on 2D axis symmetric and 3D safety simulations of flow over the benchmark DARPA SUBOFF submarine model. This webinar will discuss the 2D Axisymmetric CFT simulation of SRCCM plus, which can be an alternative to 3D CFT simulations when both the body and the flow are Axisymmetric. I will show how reliable and accurate these methods are. This particular webinar is related to a research article that my co-authors and I recently published in the peer-reviewed SC index journal, Physics of Fluid. Our co-authors are Dr. Manoj T. Issac and Dr. D. D. Ebenezer. We are all from the Computational Hydrodynamics and Structural Engineering Laboratory, Chase lab, in the Department of Ship Technology at Cochin University of Science and Technology in S.A.T. India.

This is the outline of today's webinar.

First, I will be giving an introductory section where I'll be discussing the various kinds of underwater vehicles, their classifications, and briefly explaining the methods of hydrodynamic modeling of these underwater vehicles.

Next, in the motivation section, I'll be discussing how CFD is used by designers in the initial stages of vehicle development and its drawbacks.

Moving on to the research problem section, I'll be introducing the 2D axis symmetric method and explaining what it is.

In the methodology technology section, I will explain in detail the various tests that were conducted using the 2D axis symmetric simulation.

Finally, we will discuss the research findings and score for future research work. Before moving ahead, I would like to thank all those who have helped me in successfully carrying out this research work.

It is important for listeners attending this webinar to be familiar with the fundamentals of Computational Fluid Dynamics, such as the governing equations, continuity equation, momentum equation, different schemes like implicit scheme, explicit scheme, forward differentiation method, backward differentiation method, center differentiation method, and different types of Turbulent model like cap ε K omega.

Now, this is the introductory session, so let's begin by discussing underwater vehicles. These are marine vehicles that operate beneath the surface of the sea with the main aim of executing predefined underwater missions. There are two categories of underwater vehicles: manned and unmanned. In manned vehicles, a human being is physically present inside and controls the vehicle. Examples of manned vehicles include submarines and submersibles. Submarines are designed for traveling over longer distances and larger depths, while submersibles have limitations in their operational ranges.

Moving on to unmanned underwater vehicles, they are controlled by human beings, but there is no need for a human to be physically present inside the vehicle. Examples of unmanned vehicles include Autonomous Underwater Vehicles (AUVs) and Remotely Operated Vehicles (ROVs). The difference between AUVs and ROVs is that communication between the vehicle and controller in AUVs occurs through wireless communication, while in ROVs, wired communication always exists between the operator and the vehicle. One drawback of ROVs is that they cannot travel over longer distances due to the entanglement of their wires. On the other hand, AUVs are designed to travel over longer distances and larger depths, just like submarines.

The speciality of these kinds of underwater vehicles is that they carry several onboard sensory payloads and are designed to be operated over larger depths and longer distances. This is why they are becoming a coveted technology in the fields of scientific, industrial, and military applications. In scientific applications, they are mainly used for bathymetric survey, sea mapping, biodiversity analysis, and order. In the industrial case, they are used for oil spill leakage studies and detection of oil spills. For military applications, they are used for underwater surveillance and sonar.

Some essential qualities required for these kinds of underwater vehicles include high endurance, which is the ability to travel over longer distances in a good manner.

Today, the majority of underwater vehicles in operation have a streamlined shape. This is because a streamlined shape reduces drag and allows for maximum entrance. The modern underwater vehicle is typically axisymmetric and interpreter shaped. For example, the AUV (autonomous underwater vehicle) pictured below is both axis symmetric and total shaped.

One advantage of having an interpreter shape is that if the controlled fins, used for deflecting or controlling moments of the AUV, are within the maximum diameter of the AUV, they can be launched from interpreter tubes on submarines very silently. This is why most AUVs in operation today have a top row shape.

The figure on the left is a typical survey class AUV with a streamlined and axisymmetric body section and a tail section. It also has a seven control plane in the form of an X configuration and a twin-bladed propeller.

On the right, you can see the DARPA sub submarine model. The hull part and control plane part are visible here as well. However, the control plane is in a plus configuration, also known as a cruciform configuration, and the propeller is also present.

Now, let's take a look at the various hydrodynamic modeling techniques. There are three methods: predictive, numerical, and test-based. The predictive method includes analytical and semir methods, also known as AC methods, which involve mathematical expressions. By substituting the values of the variables in these expressions, you can easily obtain the hydrodynamic parameters.

The numerical method involves using COT packages to solve the rand turbulence models. On the other hand, the test-based method is experimental and involves cap team model tests. Examples of such tests include towing tanks and wind internal experimental setups. In a controlled environment, the model is tested, while in free running tests, the model is allowed to move freely in the water with sensors attached to it.

Comparing experiments with CFD methods, it is clear that the cost and time associated with experiments are very high. In contrast, CFD allows for full-scale simulations or testing, which is not possible with experiments due to size limitations. Scaling down the model leads to scaling effects, and experiments cannot be conducted in hazardous environments. CFD, on the other hand, allows for testing in hazardous environments.

Another advantage of CFD is that more designs can be tested. If you have hundreds of designs, it would be time-consuming and costly to conduct experiments on each one. However, with CFD, this job can be done easily.

Team OK. During the initial stages of vehicle design, designers are presented with a large number of designs, often hundreds, with varying shapes of nose, tail, high forms, body ratios, and more. With so many options available, it can be difficult for designers to choose the best design.

To overcome this challenge, designers rely on the use of CFD tools to determine the optimum design. References two and three discuss the effectiveness of CFD in determining the optimum body configuration, nose and tail configuration, and high form. These simulations are carried out in 3D to choose the best length, diameter ratio, and shape for the nose, tail, and high forms.

Overall, the use of CFD tools is crucial in the vehicle design process, especially in the initial stages where a large number of design options are available.

One of the drawbacks of using 3D simulations for designing hull forms is that it is a time-consuming process that requires expensive computational facilities. Handling hundreds of designs in a lab or controlling the design of an optimum hull form out of 100 models requires a high-end computational facility that can accommodate all 3D models. Additionally, the time associated with each simulation station is also high, with 3D safety simulations taking from two days to get converged. Testing hundreds of such models can take a long time, and the job may not be completed within a short span of time.

To address this issue, the CFT community is searching for methods to reduce overall computation time from days to hours. They are looking for ways to reduce simulation time and find alternatives to 3D simulations. One such alternative is the 2D axis symmetric simulation, which is used when the body is axis symmetric and the flow is also axis symmetric.

The research problem that will be addressed in this text is the 2D axis symmetric simulation of turbulent flows. Although turbulent flows are typically three-dimensional, 2D axis symmetric CFD models can provide approximate but useful results for preliminary studies if the flow and body are axis symmetric. For example, a 2D plane can be used to represent the profile of a submarine model, which can be rotated 360 degrees to create a Syr Domain containing the submarine. The RAN model can then be solved on the 2D plane, and the resulting answers can be evaluated to determine their similarity to 3D research.

The research question that must be answered is whether these 2D axis symmetric methods are reliable and accurate compared to 3D simulation. If they are not, they cannot be used. Additionally, it is important to determine the savings in computation time and memory resources that can be achieved by using 2D axis symmetric simulation. Can it be run on ordinary computers, or does it require a larger computational facility with more cores and ram facilities?

Answering these questions will determine whether 2D axis symmetric simulation is a viable alternative to 3D zero PS simulation for axial flow cases and problems where the body is axis symmetric.

In conducting the two axis symmetric simulation, we utilized the SYM plus C MP Software from Siemens and various tests were performed. The settings we used in the star system are shown below. We employed a Rectangular Domain and the Simulation Type assis metric and stress Solve was used. The property Values of Fluid we used was water, which was kept constant. The machine type utilized Automated trimmed cells with Prism Layers.

For the various Boundary Conditions, we gave a velocity Inlet which is a Related boundary condition for the Inlet and a Pressure outlet which is a new type of boundary condition for the outlet. The Hull, which is the surface of the DARPA sub submarine model used in this study, was a wall under non-slip conditions. The Far field, which are the locations away from the surface of DARPA above, was again involved but with slip conditions and the axis at the bottom axis is This region that is the upstream region before the DARPA sub above and the downstream region after the DARPA above towards the outlet. Therefore, this region, this region, and this region were considered as an axis of rotation.

We used an S S T S stress transport K omega Turbulence model with a very low Values of wall way plus and the Solving time taken was 10 minutes. This is the total amount of time that was taken for convergence. The 2D ex symmetric simulation was run on our non-ordinary computer, which utilized up to three Cores. The Software uses and center θ the same plus.

These are the various CFP simulation processes for underwater vehicles.

The basic process for any ECFP simulation remains the same. The simulation process has stepping stones that are essential to follow. The first step is the Geometry section. In this section, the data sub submarine model has been selected, and the Geometry Parameters are represented by a Profile curve. The DPA sub is a commonly used validation model among the CFD community.

The DTRC, or David Taylor's Research Center, has published experimental research on the DPA sub, including resistance tests and experimental results from wind tunnel testing. The center has also published a report explaining the various geometrical parameters of the sub, including equations for the nose, parallel mid-body, and tail.

The next step is the Domain Shape and size. A rectangular domain was selected based on I2TCS recommendations. The physics of the problem involves fluid flow, and the water's property values at 15 degrees Celsius were taken from fresh water properties from I TTC. The Turbulence model used is K omega Turbulence model, and the Boundary Conditions are user sect and New man. The initial condition is based on the speed mentioned in the DTRC reports.

The mesh used is the Trimmed cells with Prism Layers with low values of wall Y plus. A steady flow case problem was chosen because it is a bare high case where the chance of deformation is very low.

When stopping the simulation, it is essential to monitor the drag over each iteration. The simulation was stopped at 4000 iterations when the five significant digits of drag remained constant after 500 iterations.

The convergence limit for residual power below one E power minus seven is obtained for continuity. The system process is a double precision software.

Reports were generated for drag and its components, velocity profile, coefficient of pressure, wall stress curve, and verification and validation. Post-processing generated velocity, pressure, and stress contour, velocity vectors, and streamline across the star parts sub submarine model in the 2D axisymmetric method.

Now, this is the geometry of DARPA S sub, a widely used validation model among the CFT community who lack experimental results. The experimental results of DARPA S sub are available in the public domain and are published by the David Taylor's Research Center. There are two experimental results available, one from the towing tank that corresponds to the resistance cells, and the other from the wind tunnel that corresponds to velocity profile coefficient of pressure coefficient of wall stress.

On the left-hand side, you can see the TPA sub submarine model with various parts, including the nose, parallel met body, after body, and after body cap. These are the dimensions of the various parts, and a specific number of station points have been chosen to generate the profile curve.

DTRC has published the geometry of DARPA S sub along with the equations defining each of its parts. For example, for the nose, there is a dedicated equation, and for the tail, there is a separate equation. Up to 450 of 203 153 100 number of station points in each part were taken, and about 1003 100 section points were required to define this profile. This profile of database was exported as a dot CSV file into the 3D model.

Later, this 3D model was exported to start the CP plus to carry out a 2D axis symmetric simulation.

This is the computational domain that we have used for both 2D axisymmetric and 3D simulations. On the left-hand side, you can see the domain used for the 2D axisymmetric case, while on the right-hand side, you can see the domain used for 3D simulations.

For the 2D axisymmetric simulation, the upstream length is three times the length of the body, while the downstream length is six cells, with the width of the domain being two. The inlet is a velocity inlet and the outlet is a pressure outlet. The far field is a wall under slip condition, and the surface of the DAPA sub above is also a wall under nose slip condition. The upstream and downstream regions are considered as an axis of rotation.

In the 3D domain, a cylindrical domain is used with a velocity inlet, pressure outlet, far field as a wall under slip condition, and the surface of the PP S sub above as a wall under nose slip condition. The upstream length is two times the length of the body, while the downstream length is four times the length of the body.

All of these domain dimensions are based on expert recommendations. According to the recommendations, the minimum upstream distance should be considered a cell, and the downstream distances should also be the length of the body. However, when using these distances, there is a chance of return flow occurring from the outlet. Therefore, we conducted a domain-independent study for both 2D axisymmetric and 3D simulations and found that this is the optimum size of the domain that we can consider for these simulations.

Now, this is the meshing that we have used for the 2D axis symmetric simulation. We have used refinements at the inlet, outlet, and the surface of data parts. Above the mesh, we used automated trimmed cells with prism layers. These are unstructured mesh cells that are trimmed off once they come in contact with the surface of the body of interest. They encapsulate the shape of the surface of the body. The cells in contact with the DAPA above are already heavy and once they come in contact with the DAPA, the cells closer to the surface of DAPA get trimmed off and take the shape of the surface of that part. Inlet and outlet regions represent air present in the nose and tail regions, respectively. The red color regions represent the prism layer, which is used to capture turbulent boundary layers. The prism layer distribution has a thickness of 0.052 m and is distributed throughout the mesh.

Different sizes of mesh are used for the inlet, outlet, and surface of the database above. In the space between the far field and the surface, the last layer of present layer, the cores meshing is used. The cores strategy is often using the hanging nodes that help to migrate from the final mesh to medium mesh and then again from medium mesh to cores mesh. The maximum cells QA angle obtained is 36.7 degrees, and the mesh consists of 0.78 million cells. With these mesh settings, 78% of all the cells occupy the prism layer region.

For the 3D CD simulation, we used the same trimmed cells with prism layers. The various sizes of the cells are shown, and the mesh represents the nose, tail, and cross-sectional region taken at the body of data above.

In this text, the author discusses the maximum S Q N S angles and total mesh count in a simulation. They note that if a user were to perform an S statistics analysis, they would find that 87% of all cells occupy the prism layer region. This indicates a high level of refinement, particularly in the prism layer where 75 to 90% of total cells occupy this region. These results hold true even for both 2D ex symmetric and 3D simulations.

Now, this is an all-plus distribution in the 2D axis symmetric as well as 3D simulations. The red color represents the 3D simulation, while the blue color represents the 2D axis symmetric simulation. Y wall plus is the non-dimensional size thickness of the wall of cell layer thickness, which indicates how refined the mesh is. A value less than one is considered a low Y wall plus treatment, meaning that meshing is very fine in those regions.

In the Prism layer, 75 to 90% of the cells occupy it, making it very effective in capturing the double boundary layer. The Prism layer is characterized by four parameters: the number of Prism layers, the growth rate of the Prism layers, the total thickness of the Prism layers, and the Prism layer's first cell thickness. By defining these parameters, the Prism layer can easily be constructed.

A geometrical progression in the ψ plus was used to construct these Prism layers, and as we move from 2D to 3D simulations, we can see how these parameters change. In the 2D axis symmetry, 87 Prism layers were used, while in the case of 3D, only 62 Prism layers were used. The growth rate was 1.11 in the 2D axis symmetry but increased to 1.13 in the 3D simulation, while the total thickness of the Prism layer remained constant in both cases. The Prism layer's first cell thickness was 0.623 microns in the 2D simulation and 2.82 microns in the 3D simulation, resulting in a low value of Y wall plus in the 2D simulation compared to the 3D simulation.

The total number of cells in the 2D axis symmetric simulation was only 50.78 million, while in the 3D simulation, it was 33 million. When comparing Y wall plus versus 6πL ex, which stands for the local location on the surface of data, sub both measures from the leading edge of the submarine model, and that stands for the overall length of the vehicle, we can see that in the 3D simulation, the maximum value of Y wall plus is 660.45, while in the 2D axis symmetric simulation, the maximum value of Y wall plus is 50.12 with an average value of 0.04. The cells in contact with the surface of the tapas above in the first layer of Prism layer are tiny in size.

Now, of course, any CFD study will not become valid unless and until you do a grid sensitivity analysis or a grid independent study. So we have also done a grid sensitivity analysis of grid independent study using the Richardson Extrapolation. This Richardson Extrapolation is based on REFERENCES 10 and 11 and has now become a mandatory criteria when publishing research work in many peer-reviewed journals. As reference nine has cited, this has become a very mandatory criteria. That's why, if you take any research articles related to CFD on external four cases in APR reviewed article, you can see that this Chang and extrapolation has been explained there.

In our articles, we have explained in detail this research and extrapolation. The reason why this Richardson Extrapolation is connected is that from the grid sin analysis, we are selecting the fine mesh. The case where the Bible process is less than one is obtained, that is the finest mesh. But you should also be aware of what the uncertainty is associated with your fine mesh and how far you are deviating from the ideal mesh. Ideal mesh means when your cell size is zero, then using that cell, the results that you're getting is called ideal CFT value. So such a kind of measure is called ideal mission.

There are a set of equations used in the Richardson Extrapolation to find out what is the Grid Convergence Index and Order offs. These are the two important parameters which are the end results of research and extrapolation. The equations used for calculating these parameters are explained in reference 10, 9, and 11.

Now 12.3 represents the fine medium and Cores much respectively. We have selected three different representative sizes for these grid sensitivity analyses. In my case, I'm focusing on the drag value, but drag is also dependent on the wall sea stress as well as the pressure distribution. These pressure and water cells stress are actually flow variables, velocity distribution is also considered. So these flow variables are the primary variables which are greatly affected by small changes in the cell sizes.

We have selected a near wall layer, Celtic S as the representative size since by experience, we have seen that when you change the thickness of the water ad layer thickness, there are drastic changes that are obtained in the research. We have selected three different sizes in the case of 2D axis symmetric and 3D. Then we have, for each case, calculated what is the number of Prism Layers and kept the growth rate constant.

Finally, we are actually calculating the relative error between the fine and medium mesh. So that is 770.35% in the case of 2D axis symmetric, whereas it is 1.2% in the case of 3D. The Grid Convergence Index is the parameter which indicates how far you are deviating from the fine mesh or what is the uncertainty that is associated with the fine mesh.

Now we are coming into the research section verification and validation. So this is something which confuses everyone verification and validation. Are they both the same or are they both different? So what April This REFERENCES? 10 is very important P J Roa. He has actually given a beautiful definition for this verification and validation. Verification means you are solving the equations in the right manner, but as validation means you are solving the right equation.

Verification and validation are two important steps in solving CFD setups. Verification involves checking if the CFD settings have been correctly applied, while validation involves comparing the CFD results with experimental research. To remember this, imagine solving a mathematical equation and having a teacher check your answer sheet. The teacher first checks if you have done all the steps correctly (verification) before comparing your final answer with benchmark results (validation).

In this study, the researchers conducted a resistance test to compare the CFD results obtained from 2D axis symmetry and 3D simulation with experimental results from the DTRC. The drag component consists of two parts: pressure and shear. The researchers found that 92% of the Total drag is mainly due to the shear component, while the remaining 8% is due to the pressure component. The 2D axis symmetric results showed a good agreement with the experimental results, with a maximum error of less than 6%. The relative error between the 2D and 3D results was also low, at 3%.

Overall, the study demonstrated the importance of verification and validation in CFD setups and provided valuable insights into the drag components of the tested model.

Now, I will explain the pressure and wall shear components present in the track. We began by validating the pressure component in detail. To achieve this, we created a pressure counter and compared the 2D axis symmetric research with the 3D research. The results are shown on the left and right-hand sides respectively. The air is present in the nose region and the ber in the tail region.

Both the 2D axis symmetric and 3D research obtained the stagnation point, and the relative error between the two in estimating stagnation pressure is less than 1%. Additionally, we can observe similar patterns in both the 2D axis symmetric and 3D sea simulation.

Now, this is the velocity counter obtained using the 2D axis symmetric and 3D simulation. On the left-hand side are the 2D axis symmetric results, and on the right-hand side are the 3D results. This particular velocity counter was generated for a velocity of 3.14 m per second, which corresponds to the velocity of data pass above of exper results of data pass above from the wind tunnel.

It is noticeable that the 2D asymmetric simulations are giving pretty good results compared to the 3D simulation results.

Now, this is the second level of verification and validation. In this level, the focus is on the components of drag, which are pressure and wall stress. The Coefficient of Pressure (cp) and the Coefficient of Wall Stress (θ) are validated using 2D axis-symmetric and 3D simulations. The plot of cp is on the left-hand side, while the plot of θ is on the right-hand side. The 2D axis-symmetric and 3D simulations are used to estimate the cp and θ across various positions on the surface of the database. The experimental results from DTRC tan using M wind internal are compared with other research.

Cp stands for P minus P zero by half low U square, where P is the static pressure, π zero is the stag am pressure, row is the density of the fluid, and you zero is the reference velocity. The plot of cp shows the π question of pressure on the Y-axis and X-axis is X π L. The blue color curve represents the 2D axis-symmetric, while the red color curve represents the 3D results. The experimental research from DTRC is represented by the filled circle, and its reference is shown below. The green color curve represents the CFD research from DTRC, and other present studies research of 2D axis-symmetric and three research with others like skin are compared. The black color solid color process tests are the profile of seven both.

The figure shows that there is good agreement between the present study 2D axis-symmetric and 3D research with the experimental values. The present study results are also in good agreement with the DTRC CFD research as well as the CFD research from others. At locations of X by L less than 0.8, the values of cp S are negative, and the π body ex is also less than zero, which means that this is a region of favorable pressure gradient. At locations more than 00.8, the cp values are very high, indicating an adverse pressure gradient where flow suppression is expected.

Moving on to the right-hand side, the plot shows the Coefficient of Wall Stress. Sea two is defined by two double by half row U square, where two double is a wall stress row and roden of the fluid, and user REFERENCES velocity. The legends are the same as in the previous plot. The present study 2D axis-symmetric and 3D research results are compared with experimental results from DTRC as well as results from other CFD others. The results are in good agreement with the experimental results from DTRC and the C O P results from others like skin. However, the results are varying away from the C MP research from DTRC. This is because DTRC might have conducted these C O D simulations on computation facilities, which are not so powerful, resulting in low values of π plus angle. The experimental research from D T S C is shown in the references below as reference to al, and the C O D results from other results are obtained from reference 13 and reference 14.

Now, this is the third level of verification and validation. Here, we take velocity into consideration and study the velocity distribution in detail. To do this, we select four different locations on the seven side of data pass SUBOFF, namely A, B, C, ABC, and D, which we refer to as OAOBOCO and ODO measured from the origin of the data pass SUBOFF. We then create a line probe at these locations to analyze the radial and axial velocity Phys.

To compare our results, we use both the 2D axis symmetric and 3D CFD results of the present study and compare them with the explorer obtained from DTRC from the internal. The DTRC internal results are shown in the reference tool. On the right-hand side, you can see four different plots, each corresponding to a different location. In each plot, the red curve represents the present 2D axis symmetric simulation, the dotted black curve represents the present 3D less research, and the field circle represents the experimental roses from 3D D R C.

On the Y axis of each plot, we have the normalized radius, and on the X axis, we have the normalized velocity where V R corresponds to radial velocity and U X corresponds to axial velocity. We see that the 2D axis symmetric and 3D CFD results are in very good agreement with the experimental research from DTRC, and the 2D axis symmetric and 3D CFD research are also in agreement with each other.

Thus, we have completed all three levels of verification and validation, marking the accuracy and reliability of the 2D axis symmetric results when compared to the 3D CFD simulation. If the flow is axis symmetric and the body is axis symmetric, 2D axis symmetry simulation can become a better alternative or 3D simulations.

Moving on to some of the important research findings, before that, we must see an overview of the comparison between the 2D axis symmetric and the 3D CFD simulation. We maintained a very low value of five wall plus in both the 2D axis symmetric and 3D CFD simulations, with a value of 50 for the 2D axis symmetric.

In analyzing the hydrodynamics of axis symmetric bodies like submarines and UAVs, two-dimensional (2D) axis symmetric simulation is often used. The mesh requirement in the case of 2D is much lower compared to 3D, with a mesh size of only 50.78 million. In contrast, the mesh size in 3D is much larger at 33 million. The operational velocity is designed for the highest operational velocity of dark parts above, which is 9.26 m per second.

To compute the total rat, the Mode of Computation used is the 2D axis symmetric simulation on a single machine using parallel computing on a single client with three cores. In contrast, the 3D simulation used parallel computing on two clients with six cores in total. The simulation time taken for 2D axisymmetric is only 10 minutes, while it is 56 power for 3D.

While the 2D axis symmetric results are in good agreement with experimental research, they have limitations. They cannot capture turbulence when the flow is non-axis symmetric, and they can only be used on axis symmetric bodies. For bodies like rovs, which are boxy type CCU body type bodies, 2D axis symmetric problems cannot be used.

Despite its limitations, 2D axis symmetric simulation is useful in determining the hydrodynamics of axis symmetric bodies like submarines and UAVs, especially when the angle of attack is zero. Using limited computational resources, the same problem can be evaluated within 10 minutes, demonstrating the beauty of this simulation.

Now, the scope for future research work is vast as there are numerous axis-symmetric bodies such as torpedo rocket main body missiles. These bodies have a hard form present when the control planes are kept apart, which is also torpedo-shaped, streamline and axis-symmetric. Therefore, when designing such bodies, the same axis-symmetric method can be used. Designing the bare hull is crucial as it carries sensors, battery packs, power packs, and various kinds of projection systems. Hence, an optimum design for the bare hull is necessary, and a lot of time is spent on research. To speed up such research work, the 2D axis-symmetric method can be used on AY metric bodies like Autonomous Underwater Vehicles, Submarine models, MS designs, and S. In the last few slides, we have shown how accurate and reliable these 2D axis-symmetric methods are when compared to the 3D case. Therefore, this method can become an excellent alternative to 3D for determining the optimum al value ratio and all stage optimization studies, among others.

Earlier, 3D simulation was used as input for optimization algorithms using artificial intelligence and machine learning. However, now the same 2D axis-symmetric simulation can be used as an initial test for such algorithms to run problems related to artificial intelligence and machine learning.

You can find us here. This work has been published in the peer-reviewed SCI index Journal Physics of Fluid. Recently, on January 1st, 2023, a numerical investigation of two-dimensional axis-symmetric and three-dimensional flow simulation was conducted on Oma and a water vehicle.

This paper discusses the accuracy of 2D axis-symmetric simulation results in predicting the flow physics around the benchmark vehicle called ARPA SUBOFF. This is achieved by comparing the 2D axis-symmetric results with the 3D results of the present study.

The associated publication has been shown below. These are the various references used for the work. You can check out these references. Thank you.

Thank you for attending the webinar. I appreciate your patience and hope you enjoyed it. If you have any doubts or queries regarding this research work, please feel free to reach out to me for assistance. Additionally, if you have any technical questions, I am happy to help. Thank you again.

Thank you for attending the webinar. I hope you enjoyed it. If you have any doubts or queries regarding the research work presented, please feel free to write to us at R four, Rahul four at CO Z dot ac dot in or four at R four, Rahul four at Yahoo dot co dot N. You can use either email address. If you have any questions related to the webinar, you can post them on the SY web portal.

Once again, thank you for attending the webinar and thank you to the hosting team. Have a great day. Bye.