Propeller design is crucial for underwater robots, determining their thrust and efficiency. It's a balancing act between maximizing performance and minimizing issues like cavitation. Key factors include diameter, pitch, blade shape, and number of blades.

Optimizing propellers involves considering the robot's mission, size, and operating environment. Designers use advanced tools like computational fluid dynamics and experimental testing to fine-tune propeller geometry and predict performance. The goal? Creating propellers that deliver the right mix of thrust, efficiency, and reliability for underwater missions.

Propeller Design Principles

Thrust Generation and Newton's Third Law

• Propellers generate thrust by accelerating a fluid in the opposite direction of the desired vehicle motion
  • Based on Newton's third law of motion: for every action, there is an equal and opposite reaction
  • As the propeller pushes water backward, the water pushes the propeller (and the vehicle) forward with an equal force

Propeller Design Parameters and Optimization

• Propeller design involves selecting the optimal combination of parameters to maximize thrust and efficiency while minimizing cavitation and noise
  • Key parameters include diameter, pitch, blade shape, and number of blades
  • Diameter: larger diameters generally produce more thrust but may be limited by vehicle size and available power
  • Pitch: the distance a propeller would move forward in one revolution if it were moving through a solid medium
  • Blade shape: affects hydrodynamic performance and cavitation characteristics (NACA airfoils or custom designs)
  • Number of blades: typically ranges from 2 to 7, with more blades reducing cavitation and noise but potentially decreasing efficiency

Blade Element Momentum Theory (BEMT) and Performance Coefficients

• BEMT is a widely used method for analyzing and designing propellers
  • Combines blade element theory (analyzes forces on individual blade sections) and momentum theory (considers conservation of fluid momentum)
  • Allows for the prediction of propeller performance characteristics and optimization of blade geometry
• Propeller performance is characterized by dimensionless coefficients
  • Advance ratio (J): relates the vehicle's speed, propeller rotational speed, and diameter
  • Thrust coefficient (KT): represents the thrust generated by the propeller
  • Torque coefficient (KQ): represents the torque required to rotate the propeller
  • Efficiency (η): the ratio of output power (thrust × velocity) to input power (torque × rotational speed)

Propeller Geometry and Operating Environment

• Propeller geometry parameters have a significant impact on performance and cavitation
  • Pitch (P): the axial distance traveled by the propeller in one revolution, often expressed as a ratio of pitch to diameter (P/D)
  • Expanded area ratio (EAR): the ratio of the total blade area to the propeller disc area
  • Skew: the angular displacement of the blade sections along the propeller's axis, which can help reduce cavitation and noise
  • Rake: the axial displacement of the blade sections, which can improve hydrodynamic performance and structural strength
• The propeller's operating environment must be considered in the design process
  • Vehicle's speed range: affects the advance ratio and the propeller's efficiency and cavitation characteristics
  • Operating depth: influences the local pressure and the risk of cavitation
  • Water properties: density and viscosity affect the propeller's thrust, torque, and efficiency

Propeller Efficiency and Thrust

Propeller Efficiency and Power

• Propeller efficiency (η) is a key performance metric that indicates how effectively the propeller converts input power to output power
  • Output power is the product of thrust and velocity: $P_out = T × V$
  • Input power is the product of torque and rotational speed: $P_in = Q × ω$, where $ω$ is in radians per second
  • Efficiency is the ratio of output power to input power: $η = P_out / P_in = (T × V) / (Q × ω)$
• Open-water propeller efficiency (ηo) can be calculated from the thrust coefficient (KT), torque coefficient (KQ), and advance ratio (J)
  • $ηo = (J × KT) / (2π × KQ)$
  • This efficiency represents the propeller's performance in undisturbed flow, without the influence of the vehicle's hull or appendages

Thrust and Torque Calculations

• Thrust (T) can be calculated using the thrust coefficient (KT), water density (ρ), rotational speed (n), and propeller diameter (D)
  • $T = KT × ρ × n^2 × D^4$, where n is in revolutions per second
  • The thrust coefficient (KT) is a dimensionless number that depends on the propeller's geometry and operating conditions
• Torque (Q) can be calculated using the torque coefficient (KQ), water density (ρ), rotational speed (n), and propeller diameter (D)
  • $Q = KQ × ρ × n^2 × D^5$
  • The torque coefficient (KQ) is a dimensionless number that depends on the propeller's geometry and operating conditions

Propeller Performance Curves and Prediction Methods

• Propeller performance curves, such as KT and KQ versus J, can be used to predict thrust, torque, and efficiency at various operating conditions
  • These curves are typically obtained from experimental tests (towing tank or cavitation tunnel) or numerical simulations (CFD)
  • By knowing the vehicle's speed, propeller diameter, and rotational speed, the advance ratio (J) can be calculated, and the corresponding KT, KQ, and efficiency values can be determined from the performance curves
• Computational fluid dynamics (CFD) and experimental methods can be used to refine and validate propeller performance predictions
  • CFD simulations solve the governing equations of fluid motion (Navier-Stokes equations) to predict the flow field around the propeller and calculate the resulting forces and moments
  • Experimental methods, such as towing tank tests or cavitation tunnel tests, measure the propeller's thrust, torque, and efficiency under controlled conditions
  • These methods help to optimize the propeller design and validate the numerical predictions

Propeller Geometry Effects

Pitch and Expanded Area Ratio

• Pitch-to-diameter ratio (P/D) affects the propeller's efficiency, thrust, and cavitation characteristics
  • Higher P/D ratios generally increase efficiency by allowing the propeller to operate at a higher advance ratio (J) for a given speed and rotational speed
  • However, high P/D ratios may lead to cavitation at high speeds due to the increased local velocities and reduced pressures on the blade surfaces
• Expanded area ratio (EAR) is the ratio of the total blade area to the propeller disc area
  • Higher EAR can reduce cavitation by distributing the thrust over a larger blade area, thus reducing the local loading and the risk of low-pressure regions
  • However, higher EAR may also decrease efficiency due to increased friction drag on the blades

Blade Number and Geometry

• Blade number affects the propeller's efficiency, cavitation, and noise characteristics
  • Increasing blade number generally reduces cavitation and noise by distributing the thrust over more blades and reducing the loading on each blade
  • However, increasing blade number may also decrease efficiency due to increased friction drag and interference between the blades
  • Common blade numbers range from 2 to 7, with 3 to 5 blades being the most common for underwater vehicles
• Skew and rake angles can be used to optimize propeller performance and reduce cavitation
  • Skew is the angular displacement of the blade sections along the propeller's axis, which can help to reduce cavitation and noise by aligning the blade sections with the local inflow velocity and reducing the sudden changes in loading
  • Rake is the axial displacement of the blade sections, which can improve hydrodynamic performance by aligning the blade sections with the flow and reducing the angle of attack, as well as improving structural strength by distributing the bending moments more evenly along the blade

Blade Section Shape and Cavitation

• Blade section shape (e.g., camber, thickness, and leading-edge radius) influences the propeller's hydrodynamic performance and cavitation inception
  • Camber (curvature) of the blade section affects the lift and drag characteristics, with higher camber generally increasing lift but also increasing the risk of cavitation due to the lower pressures on the suction side
  • Thickness of the blade section affects the structural strength and the pressure distribution, with thicker sections generally being more resistant to cavitation but also having higher drag
  • Leading-edge radius affects the pressure distribution and the cavitation inception, with larger radii reducing the risk of cavitation by minimizing the peak suction pressures near the leading edge
• Cavitation occurs when the local pressure drops below the vapor pressure of water, forming vapor bubbles that can cause performance loss, erosion, and noise
  • Cavitation number (σ) relates the local pressure (p), vapor pressure (pv), and fluid velocity (V) as: $σ = (p - pv) / (0.5 × ρ × V^2)$
  • Lower cavitation numbers indicate a higher likelihood of cavitation, as the local pressure is closer to the vapor pressure
• Cavitation inception charts and criteria (e.g., Burrill's criterion) can be used to predict and avoid cavitation based on the propeller's geometry and operating conditions
  • These charts and criteria relate the cavitation number to the blade section's lift coefficient or the propeller's thrust coefficient, providing a threshold for cavitation inception
  • By designing the propeller to operate below the cavitation inception threshold, the risk of cavitation can be minimized

Propeller Optimization for Robots

Mission Requirements and Propulsion System Selection

• Define the vehicle's mission requirements, including speed range, payload, endurance, and operating depth
  • Speed range: determines the required thrust and the propeller's operating advance ratio (J)
  • Payload: affects the vehicle's weight and the required thrust to achieve the desired speed
  • Endurance: influences the propulsion system's efficiency and the energy storage requirements
  • Operating depth: affects the ambient pressure and the risk of cavitation
• Select the appropriate propulsion system based on the vehicle's size, speed, and maneuverability requirements
  • Single propeller: simple and efficient, suitable for vehicles with moderate speed and maneuverability requirements
  • Contra-rotating propellers: provide higher thrust and efficiency by recovering the rotational energy in the wake, suitable for vehicles with high speed and thrust requirements
  • Ducted propellers: provide higher thrust at low speeds and improved efficiency by reducing tip losses, suitable for vehicles with high maneuverability and hovering requirements

Propeller Sizing and Blade Geometry Optimization

• Determine the optimal propeller diameter and rotational speed range based on the vehicle's thrust requirements, available power, and space constraints
  • Larger diameters generally produce more thrust but may be limited by the vehicle's size and the clearance between the propeller and the hull
  • Higher rotational speeds generally reduce the required propeller diameter but may be limited by the motor's power and the risk of cavitation
• Choose the appropriate blade number, pitch, and expanded area ratio to maximize efficiency and thrust while minimizing cavitation risk for the given operating conditions
  • Blade number: typically 3 to 5 for underwater vehicles, with more blades reducing cavitation and noise but potentially decreasing efficiency
  • Pitch-to-diameter ratio (P/D): typically 0.8 to 1.4, with higher ratios increasing efficiency but also increasing the risk of cavitation at high speeds
  • Expanded area ratio (EAR): typically 0.5 to 1.0, with higher ratios reducing cavitation but also potentially decreasing efficiency
• Optimize blade section shape and radial distribution of pitch, chord length, and thickness to achieve the desired hydrodynamic performance and structural integrity
  • Blade section shape: use high-lift, low-drag sections (e.g., NACA 16 or 66 series) with appropriate camber, thickness, and leading-edge radius to maximize efficiency and minimize cavitation risk
  • Radial distribution: use variable pitch and chord length to optimize the load distribution along the blade, with higher pitch and longer chords near the root and lower pitch and shorter chords near the tip

Integration and Validation

• Consider the propeller's material selection and manufacturing process based on the required strength, durability, and cost
  • Common materials include stainless steel, aluminum alloys, and fiber-reinforced composites (e.g., carbon fiber or glass fiber)
  • Manufacturing processes include metal casting, CNC machining, composite layup, and 3D printing (e.g., selective laser sintering or fused deposition modeling)
• Integrate the propeller design with the vehicle's hull form, control surfaces, and propulsion system components to ensure compatibility and performance
  • Hull form: optimize the hull shape to minimize drag and improve the inflow to the propeller, using computational fluid dynamics (CFD) and experimental testing (e.g., towing tank tests)
  • Control surfaces: design the control surfaces (e.g., rudders, fins, or ducts) to provide the required maneuverability and stability while minimizing their interference with the propeller
  • Propulsion system components: select the appropriate motor, gearbox, shafts, bearings, and seals to transmit the propeller's torque and thrust efficiently and reliably
• Validate the propeller design through numerical simulations, experimental testing, and in-situ trials to assess performance and refine the design if necessary
  • Numerical simulations: use CFD to predict the propeller's performance, cavitation, and noise characteristics under various operating conditions
  • Experimental testing: conduct towing tank or cavitation tunnel tests to measure the propeller's thrust, torque, and efficiency, and to visualize the cavitation patterns and tip vortices
  • In-situ trials: test the propeller on the actual vehicle in its intended operating environment to assess its performance, maneuverability, and reliability, and to identify any potential issues or areas for improvement