🫠Underwater Robotics Unit 2 – Hydrodynamics for Underwater Vehicles

Fluid Dynamics Fundamentals

• Fluid dynamics studies the behavior and motion of liquids and gases, essential for understanding how underwater vehicles move through water
• Key properties of fluids include density, viscosity, and compressibility, which affect how they interact with objects moving through them
• Bernoulli's principle states that as fluid velocity increases, pressure decreases, explaining phenomena like lift and drag (airfoils, hydrofoils)
• Reynold's number is a dimensionless quantity that characterizes flow regime as laminar, transitional, or turbulent based on fluid properties and flow conditions
  • Laminar flow occurs at low Reynold's numbers and is characterized by smooth, parallel streamlines (small UUVs at low speeds)
  • Turbulent flow occurs at high Reynold's numbers and features chaotic, swirling motion with increased mixing and drag (larger UUVs at high speeds)
• Navier-Stokes equations are a set of partial differential equations that describe the motion of viscous fluids, but are computationally expensive to solve directly
• Boundary layers form near surfaces where fluid velocity drops to zero, influencing drag and heat transfer (UUV hulls, control surfaces)

Underwater Vehicle Design Principles

• Streamlining reduces drag by minimizing flow separation and turbulence, achieved through smooth, gradually tapering shapes (torpedoes, submarines)
• Pressure hulls must withstand hydrostatic pressure at depth while minimizing weight, often using cylindrical or spherical shapes and high-strength materials (titanium, composites)
• Buoyancy and stability are controlled by adjusting the vehicle's weight and center of gravity relative to the center of buoyancy
  • Positive buoyancy causes ascent, negative buoyancy causes descent, and neutral buoyancy allows hovering at a constant depth
• Control surfaces such as fins, rudders, and hydroplanes alter the vehicle's orientation and trajectory by generating lift forces in the fluid
• Modularity and redundancy improve reliability and adaptability, allowing components to be easily replaced or reconfigured for different missions
• Efficient propulsion systems are critical for long-range operations, often using propellers, thrusters, or biomimetic designs (fish-like swimming)
• Sensors and payloads must be carefully integrated to maintain hydrodynamic efficiency while providing necessary functionality (cameras, sonars, manipulators)

Propulsion Systems and Efficiency

• Propellers generate thrust by accelerating fluid backwards, with efficiency dependent on factors like blade shape, pitch, and rotational speed
  • Ducted propellers (kort nozzles) improve efficiency and protect blades but add complexity and weight
• Thrusters provide maneuvering forces in multiple directions, allowing hovering and precise control at low speeds (ROVs, AUVs)
• Jet propulsion systems expel water at high velocity to generate thrust, offering high power density but lower efficiency than propellers
• Biomimetic propulsion seeks to emulate efficient swimming motions of aquatic animals using undulating fins or oscillating foils (robotic fish, tuna-inspired designs)
• Efficiency is maximized by matching propulsion system characteristics to the vehicle's operating speed, depth, and mission requirements
• Electric motors are commonly used for underwater propulsion due to their reliability, controllability, and lack of exhaust (battery-powered UUVs)
• Thermal engines like diesel generators or fuel cells can extend range but require air supply or exhaust management (submarines, hybrid UUVs)

Drag and Resistance in Water

• Drag forces oppose motion through water, consisting of friction drag (skin friction) and pressure drag (form drag)
  • Friction drag arises from fluid viscosity and increases with wetted surface area and roughness (biofouling, corrosion)
  • Pressure drag results from flow separation and wake formation behind bluff bodies, increasing with cross-sectional area and bluntness
• Wave-making resistance is an additional drag component for vehicles operating near the water's surface, caused by energy dissipation in generated waves
• Drag increases quadratically with velocity ($F_D = \frac{1}{2} \rho v^2 C_D A$), so doubling speed requires four times the thrust to maintain
• Streamlining and smooth surfaces minimize drag by delaying flow separation and reducing turbulence (laminar flow hulls, fairings)
• Appendages like sensors, antennas, and control surfaces add parasitic drag, so they must be carefully designed and integrated
• Coatings and materials can help reduce skin friction and biofouling, but may require frequent cleaning or replacement (antifouling paint, hydrophobic surfaces)
• Active flow control techniques like boundary layer suction or injection can further reduce drag but add complexity and power requirements

Stability and Maneuverability

• Static stability ensures a vehicle returns to its original orientation after small disturbances, achieved through careful weight distribution and buoyancy control
  • Metacentric height is the distance between the center of gravity and the metacenter (point of intersection between buoyant force and vertical centerline), with a positive value indicating stability
• Dynamic stability considers the vehicle's response to larger disturbances or deliberate maneuvers, influenced by factors like moment of inertia and control surface effectiveness
• Maneuverability is the ability to change speed, depth, and heading rapidly and accurately, important for obstacle avoidance, target tracking, and station-keeping
• Control algorithms and autopilots help maintain stability and execute maneuvers by adjusting control surfaces, propulsion, and buoyancy (PID controllers, model predictive control)
• Passive stabilization techniques use fixed fins or keels to provide self-righting moments without active control (pendulum-based systems, buoyancy-driven mechanisms)
• Hovering and low-speed maneuverability require precise control of forces and moments in multiple degrees of freedom, often using thrusters or variable buoyancy systems
• Testing in water tanks or computer simulations helps validate stability and maneuverability before real-world deployment

Sensors and Navigation in Fluid Environments

• Acoustic sensors like sonar provide underwater perception and ranging by emitting sound waves and detecting echoes from obstacles or targets
  • Multibeam and side-scan sonars generate detailed maps of the seafloor or underwater structures
  • Doppler velocity logs (DVLs) measure the vehicle's speed over ground by analyzing the frequency shift of acoustic reflections
• Optical sensors like cameras and laser scanners offer high-resolution imagery but are limited by water clarity and light absorption (turbidity, color distortion)
• Inertial navigation systems (INS) estimate the vehicle's position, velocity, and orientation by integrating accelerometer and gyroscope measurements over time
  • Drift errors accumulate without external references, so INS is often combined with other sensors like GPS or acoustic beacons
• Pressure sensors measure water depth and help maintain depth control, while temperature and conductivity sensors provide data on the fluid environment
• Magnetometers detect the Earth's magnetic field for heading reference, but are subject to interference from the vehicle's own magnetic signature
• Sensor fusion algorithms like Kalman filters combine measurements from multiple sensors to improve accuracy and robustness
• Acoustic communication allows data exchange and remote control, but has limited bandwidth and range due to signal attenuation in water

Computational Fluid Dynamics for UUVs

• Computational Fluid Dynamics (CFD) simulates fluid flow around vehicles using numerical methods to solve governing equations like Navier-Stokes
• CFD allows designers to predict hydrodynamic forces, optimize shapes, and test performance in virtual environments before building physical prototypes
• Mesh generation discretizes the fluid domain into small elements or volumes, with finer resolution needed near surfaces and in high-gradient regions (boundary layers, vortices)
• Turbulence modeling approximates the effects of small-scale fluctuations on the mean flow, using techniques like Reynolds-Averaged Navier-Stokes (RANS) or Large Eddy Simulation (LES)
  • RANS models add turbulence transport equations to the Navier-Stokes equations, while LES directly resolves large-scale turbulent structures and models sub-grid scales
• Boundary conditions specify fluid properties and flow conditions at the domain boundaries, such as inlet velocity, outlet pressure, or wall no-slip
• Post-processing visualizes and analyzes CFD results, generating contours, streamlines, or force plots to gain insights into flow patterns and vehicle performance
• Validation compares CFD predictions with experimental data or analytical solutions to assess accuracy and identify modeling limitations
• Optimization methods like adjoint-based shape optimization or evolutionary algorithms can automatically improve designs based on CFD-derived objectives (drag reduction, propulsive efficiency)

Real-World Applications and Case Studies

• Autonomous underwater vehicles (AUVs) perform long-range oceanographic surveys, seafloor mapping, and environmental monitoring without human intervention (Slocum gliders, Tethys LRAUV)
• Remotely operated vehicles (ROVs) are tethered to a surface ship and piloted by humans for tasks like underwater inspection, maintenance, and recovery (Hercules ROV, Nereus hybrid ROV/AUV)
• Underwater gliders use variable buoyancy and wings to achieve efficient, long-duration flight-like motion for persistent sampling and surveillance (Spray glider, Seaglider)
• Biomimetic robots emulate the efficient swimming motion of fish, mammals, or microorganisms using flexible structures and unconventional propulsion (Robotuna, Sepios octopus-inspired robot)
• Swarm robotics deploys multiple coordinated UUVs to perform distributed sensing, mapping, or manipulation tasks, inspired by schooling fish or swarming insects (CoCoRo project, MONSUN II)
• Intervention AUVs combine the autonomy of AUVs with the manipulation capabilities of ROVs, enabling complex tasks like valve turning or sample retrieval without a tether (SAUVIM, DexROV)
• Underwater docking and recharging stations extend the operational range and duration of UUVs by providing power and data transfer without surfacing (Bluefin HAUV, Hydroid REMUS)
• Hybrid vehicles blend the capabilities of different UUV types, such as combining glider efficiency with thruster-based maneuverability or hover (Aqua2 vehicle, Naviator air/water drone)