# Fluid Mechanics Applications/Aabdoz: Underwater Vehicle Design

As the name indicates underwater vehicle is the vehicle which travels underwater with or without requiring input from an operator/pilot. Underwater vehicles (UVs) have the potential to revolutionize our access to the oceans to address critical problems such as underwater search and mapping, climate change assessment, marine habitat monitoring, and shallow water mine countermeasures. They can measure physical characteristics of water, such as temperature, salinity, and dissolved oxygen, detect chlorophyll from microscopic marine algae, and measure concentrations of small particles in water, map the seafloor, and collect the images of the sea floor and the mid water. They have the potential to become ubiquitous tool for ocean exploration and sampling. Underwater vehicles are grouped into two main categories: Manned Underwater Vehicles or MUVs in short, and Unmanned Underwater Vehicles (UUVs in brief). While MUVs are able to operate underwater with a human occupant (such as submarine), UUVs are able to operate without a human occupant. [1]

ROV design
ROV animated view

## History

During the Middle-Ages, the Englishman William Bourne designed a prototype submarine in 1578. The first successful submarine was built in 1620 by Cornelius Jacobszoon Drebbel, it may have been based on Bourne's design. The origin of AUV’s should probably be linked to the Whitehead Automobile “Fish” Torpedo. Robert Whitehead is credited with designing, building, and demonstrating the first Torpedo in Austria in 1866.[2] The need to obtain oceanographic data along precise trajectories and under ice motivated Stan Murphy, Bob Francois, and later Terry Ewart of the Applied Physics Laboratory of the University of Washington to begin development of what may have been first “True” AUV in the late 1950’s. Their work led to the development and operation of The Self Propelled Underwater Research Vehicle(s) (SPURV). SPURV I, became operational in the early 60’s and supported research efforts through the mid 70’s.[3]

## Applications

RoV Operations will reduce expensive and dangerous diver deployment. The following applications are ideal for our RoVs within the offshore, onshore, and inshore environments.All feasible surveys, inspections, surveillance and light intervention work under water in areas such as:

• Oil & Gas Industry
• Aquaculture
• Salvage, recovery and rescue
• Chemical Industries
• Cooling water intakes and outlets
• Corrosion and cathodic measurements
• Detection of objects (anticollision / imaging sonar and side scan sonar)
• Sample taking
• Reservoirs / dams
• Enclosures, pipes, cable
• Environmental investigations
• Investigating sunken objects (ships, wrecks, cars, motorbikes, aeroplanes etc)

## Center of Buoyancy

The calculation of center of buoyancy has been performed considering the total volume of underwater vehicle. The equation for calculating ${\displaystyle X_{b}}$  is given below:

${\displaystyle x_{b}={\frac {(x\forall )_{thruster}+(x\forall )_{cylinder}+(x\forall )_{wings}}{(\forall _{thruster}+\forall _{cylinder}+\forall _{wings})}}}$

• ${\displaystyle x}$ - Distance of individual volume from x-z plane
• ${\displaystyle x_{b}}$ - Distance of center of buoyancy from of x-z plane
• ${\displaystyle \forall }$ - Volume of different sections of vehicle

## Center of gravity

The center of gravity (C.G) is calculated by considering weights of each component from center of cylinder which coincides with the origin of ${\displaystyle X_{v}}$ ${\displaystyle Z_{v}}$  plane.

${\displaystyle x_{cg}={\frac {(xm)_{thruster}+(xm)_{cylinder}+(xm)_{wings}}{(m_{thruster}+m_{cylinder}+m_{wings})}}}$

${\displaystyle z_{cg}={\frac {(zm)_{thruster}+(zm)_{cylinder}+(zm)_{wings}}{(m_{thruster}+m_{cylinder}+m_{wings})}}}$

• ${\displaystyle x_{cg}}$ –Center of gravity in x-direction
• ${\displaystyle z_{cg}}$ –Center of gravity in z-direction
• ${\displaystyle x}$ -Distance from center of X-Z plane
• ${\displaystyle z}$ -Distance from center of X-Z plane
• ${\displaystyle m}$ -Mass of components

## Thrust Equation

Thrust is the force applied by the volume of fluid passed at the discharge of the fan. the basic equation is given by

${\displaystyle T_{g}=Q_{d}\times V_{d}\times \rho }$

${\displaystyle T_{g}}$  = Gross thrust (exclusive drag or losses)

${\displaystyle Q_{d}}$  = Quantity of air at discharge

${\displaystyle V_{d}}$  = velocity of air at discharge

${\displaystyle \rho }$  = density of fluid

Momentum drag

A thrust fan works by taking still fluid from in front of it and using the fan blades to increase the pressure and velocity.If the fluid at the inlet already has some momentum the fan is unable to increase its velocity by the same amount, this difference is refereed as momentum drag ${\displaystyle (D_{m})}$

${\displaystyle D_{m}=Q_{d}\times V_{o}\times \rho }$

${\displaystyle V_{o}}$  = free stream velocity

Net thrust

Net thrust ${\displaystyle (T_{n})}$  is the gross thrust less than the momentum drag

Therefore net thrust is given by

${\displaystyle T_{n}=(Q_{d}\times V_{d}\times \rho )-(Q_{d}\times V_{o}\times \rho )}$

${\displaystyle T_{n}=Q_{d}\times \rho (V_{d}-V_{o})}$

The quantity of fluid is given by fan Area ${\displaystyle \times }$  discharge velocity ${\displaystyle (A\times V_{d})}$

 ${\displaystyle T_{g}=V_{d}^{2}\times A\times \rho Newtons}$

 ${\displaystyle T_{n}=V_{d}\times A\times \rho (V_{d}-V_{o})Newtons}$


2D view of propeller section

Integral Approach

The control volume shown in Figure has been drawn far enough from the device so that the pressure is everywhere equal to a constant. This is not required, but it makes it more convenient to apply the integral momentum theorem. We will also assume that the flow outside of the propeller streamtube does not have any change in total pressure. Then since the flow is steady we apply:

${\displaystyle \sum F_{x}=\int \limits _{cs}u_{x}\rho {\vec {u}}\cdot {\vec {n}}\mathrm {d} s}$

Since the pressure forces everywhere are balanced, then the only force on the control volume is due to the change in momentum flux across its boundaries. Thus by inspection, we can say that

${\displaystyle T={\dot {m}}(u_{e}-u_{o})}$

${\displaystyle T=\int \limits _{cs}\rho u_{x}({\vec {u}}\cdot {\vec {n}})\mathrm {d} A}$

${\displaystyle \int \limits _{cs}u_{x}\rho {\vec {u}}\cdot {\vec {n}}\mathrm {d} A=\rho _{e}u_{e}A_{e}u_{e}-\rho _{o}u_{o}A_{o}u_{o}+\int \limits _{cs-A_{o}-A_{e}}u_{x}\rho {\vec {u}}\cdot {\vec {n}}\mathrm {d} A={\dot {m}}u_{e}-{\dot {m}}u_{o}+{\vec {u_{o}}}\cdot \int \limits _{cs-A_{o}-A_{e}}\rho u_{x}({\vec {u}}\cdot {\vec {n}})\mathrm {d} A}$

Note that the last term is identically equal to zero by conservation of mass. If the mass flow in and out of the propeller streamtube are the same (as we have defined), then the net mass flux into the rest of the control volume must also be zero.

So we have:

${\displaystyle T={\dot {m}}(u_{e}-u_{o})}$

## Visual Analysis

The various flow visualization shown is made in the Solidworks platform. Flow Simulation enables engineers to take advantage of CAD integration, advanced geometry meshing capabilities, powerful solution convergence, and automatic fl ow regime determination without sacrificing ease of use or accuracy. Product engineers and CFD experts alike, armed with the power of SOLIDWORKS Flow Simulation, can predict flow fi elds, mixing processes, and heat transfer, and directly determine pressure drop, comfort parameters, fluid forces, and fluid structure interaction during design. SOLIDWORKS Flow Simulation enables true concurrent CFD, without the need for advanced CFD expertise. SOLIDWORKS Flow Simulation software takes the complexity out of flow analysis and enables engineers to easily simulate fl uid fl ow, heat transfer, and fluid forces so engineers can investigate the impact of a liquid or gas fl ow on product performance.

Dynamic pressure on propeller

Pressure variation on propeller

Velocity variation on rotating propeller

## References

1. Undersea Vehicles and National Needs, Committee on Undersea Vehicles and National Needs, Marine Board, Commission on Engineering and Technological Systems, National Research Council, National Academy Press, Washington D.C. 1996.
2. Ewart, T. E., “Observations from Straight Line Isobaric Runs of SPURV”, Joint Oceanography Assembly; Edinburgh (UK), 13 Sep. 1976.
3. Michel, J. L., and Le Roux, H., “Epulard: Deep bottom surveys now with acoustic remote controlled vehicle, First Operational Experience”, Proceedings of Oceans ’81 September 16–18, 1981, Boston, MA Pp 99-103.