Coupled hydro-aero-turbo dynamics of liquid-tank system for wave energy harvesting: Numerical modellings and scaled prototype tests

This study proposes and validates a novel integrated numerical model for wave-energy-harvesting liquid tanks equipped with multi-layered impulse air turbines, revealing that optimizing turbine design and tank breadth significantly enhances power output while multi-layered configurations offer superior reliability in extreme conditions compared to conventional single-rotor systems.

The Gist

The Big Idea: A "Wave-Powered Coffee Maker" in the Ocean

Imagine you want to generate electricity from ocean waves. Usually, engineers build machines that stick out of the water, like a giant floating buoy with moving parts (gears, pistons, turbines) exposed to the salty, corrosive sea. The problem? The ocean is a harsh environment. Saltwater rusts metal, giant storms smash delicate parts, and keeping these machines running for 20 years is a nightmare.

This paper proposes a clever solution: The "Enclosed" Wave Tank.

Think of this device not as a machine sticking out of the water, but as a sealed, underwater coffee maker.

1. The Pot: A large, hollow, hydrofoil-shaped buoy floats on the surface.
2. The Liquid: Inside the buoy, there are U-shaped tanks filled with water.
3. The Heat (The Wave): As the ocean waves push the buoy up and down, the water inside the tank sloshes back and forth, just like coffee in a cup when you walk with it.
4. The Steam (The Air): As the water sloshes, it pushes air back and forth through a pipe connecting the two sides of the tank.
5. The Turbine: Inside that air pipe, there is a special fan (turbine) that spins whenever the air moves, generating electricity.

The genius here is that all the moving parts are hidden inside the dry, sealed hull. The ocean can crash over the top, but the delicate electronics and gears are safe and dry inside.

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The Problem They Solved: The "Traffic Jam" in the Air Pipe

The researchers realized that while this "sealed" idea is great for durability, it had a major flaw: Efficiency.

Imagine trying to blow air through a narrow straw to spin a pinwheel. If the straw is too narrow or the pinwheel is too stiff, the air just bounces off, and the pinwheel spins slowly. In previous designs, the water sloshing would push the air, but the air couldn't push the turbine hard enough to make much power. It was like trying to power a car engine with a gentle breeze.

To fix this, they invented something called MLATS (Multi-Layered Impulse Air Turbine Systems).

The Analogy:

• Old Design (Single Rotor): Imagine a single windmill in a hallway. If the wind blows one way, it spins. If it blows the other way, it spins the same way. But if the wind is weak, it doesn't spin fast.
• New Design (MLATS): Imagine a hallway with three windmills stacked one after another, like a relay race team.
  • The air hits the first fan, spins it, and then the air (still moving fast) hits the second fan, then the third.
  • Even if the air slows down a bit after the first fan, the second and third fans catch the remaining energy.
  • It's like having three people pushing a stalled car instead of just one. You get much more power out of the same amount of wind.

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What They Did: The "Virtual" and "Real" Tests

The team didn't just guess; they built a super-complex computer simulation and a physical model to prove it works.

1. The Computer Simulation (The "Digital Twin"):
   They created a virtual world where they could simulate water sloshing, air compressing, and turbines spinning all at the same time. This is hard to do because water, air, and metal all behave differently. They had to write a new "rulebook" (math model) to make the computer understand how these three things talk to each other.

2. The Physical Model (The "Shaking Table"):
   They built a small-scale version of their device in a lab. They put it on a giant shaking table (like a giant version of a washing machine's spin cycle) to mimic ocean waves. They used cameras and sensors to watch the water slosh and the air pressure change, comparing the real results to their computer predictions.

The Result: The computer was spot-on. It predicted exactly how fast the fan would spin and how high the water would rise. This means their "Digital Twin" is reliable for designing the real thing.

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Key Discoveries: What Makes It Work Best?

Through their tests, they found some surprising rules:

• The "Heavy Flywheel" Effect: They found that making the turbine blades heavier (increasing the "moment of inertia") didn't make it spin faster, but it made the speed much smoother. It's like a heavy flywheel on an old steam engine; it doesn't speed up instantly, but once it's moving, it keeps a steady rhythm even if the wind gusts.
• The "Goldilocks" Damping: The electrical resistance (damping) needs to be just right.
  • Too little resistance: The fan spins wildly fast but generates almost no electricity (like a car in neutral).
  • Too much resistance: The fan is too hard to turn, so it barely spins at all.
  • Just right: They found the "sweet spot" where the fan spins at a steady speed and generates maximum power.
• The "Wider Tank" Trick: They discovered that making the water tank wider (doubling its width) didn't just double the power—it quadrupled it! This is a "non-linear" boost, meaning a small change in size leads to a huge jump in energy.
• The "Backup Plan" (Reliability): This is the most exciting part.
  • In old single-turbine systems, if the fan breaks, the whole machine stops working.
  • In their new 3-layer system, if the middle fan breaks, the machine still produces 78% of its power. If an outer fan breaks, it still produces 56%.
  • Analogy: Imagine a three-engine airplane. If one engine fails, the plane can still fly. If it were a single-engine plane, a failure would be a crash. This new design is "fail-safe."

The Bottom Line

This paper introduces a wave energy device that is tougher (because the parts are hidden inside), smarter (using a multi-layered fan system to capture more energy), and safer (if one part breaks, the others keep working).

They proved that by hiding the mechanics inside a water-filled tank and using a "relay team" of fans, we can harvest ocean energy much more efficiently than before. It's a significant step toward making wave power a reliable, real-world energy source that can survive the harshest storms.

Technical Summary

1. Problem Statement

Ocean wave energy conversion (WEC) faces significant challenges regarding survivability and efficiency.

• Survivability: Conventional WECs (e.g., Oscillating Water Columns, Point Absorbers) often expose critical mechanical and electrical components (turbines, generators, hinges) to the harsh marine environment (saltwater, corrosion, extreme wave slamming). This leads to frequent technical failures and high maintenance costs.
• Efficiency: Existing "enclosed" WECs (En-WECs) that hide components inside a hull often suffer from low energy conversion efficiency. Specifically, pneumatic liquid-tank systems (where sloshing liquid drives air turbines) have shown poor Capture Width Ratios (CWR) in previous studies.
• Knowledge Gap: There is a lack of integrated studies on the coupled hydro-aero-turbo dynamics of these systems. Previous models often simplified the turbine as a perforated plate, failing to capture the complex, simultaneous interactions between liquid sloshing, compressible air flow, and turbine rotor mechanics.

2. Methodology

The authors developed a comprehensive approach combining advanced numerical modeling with physical experimentation.

A. Integrated Numerical Model

• Governing Equations: The model solves the Reynolds-Averaged Navier-Stokes (RANS) equations for both liquid and air phases. The air is treated as a compressible ideal gas.
• Coupling Strategy: The fluid domain is divided into a hydro-aero region (liquid tank and air chambers) and $N$ aero-turbo regions (surrounding each turbine rotor).
  • A bidirectional data transfer occurs at the interfaces between regions, allowing for the exchange of mass, momentum, and energy.
  • The turbine rotors rotate passively based on the pressure difference across them, governed by Newton's second law ($J\dot{\omega} = T_a - T_r$), where $T_r$ includes inherent resistance and Power Take-Off (PTO) damping.
• Software: Implemented using StarCCM+ with the Finite Volume Method (FVM), SIMPLE algorithm for pressure-velocity coupling, and the HRIC method for free-surface capturing.
• Validation: A scaled physical prototype (1:1 scale for the tank, specific scaling for the turbine) was built using PMMA plates and 3D-printed resin turbines. It was tested on a 6-DOF shaking table to simulate surge motion, with measurements taken via ultrasonic wave gauges, pressure sensors, and a servo motor acting as a load/speed sensor.

B. Multi-Layered Impulse Air Turbine Systems (MLATS)

To address efficiency issues, the study introduced a novel MLATS design replacing conventional single-rotor Wells turbines.

• Design: The system features multiple layers of rotors (1, 2, or 3 layers) installed in an air duct connecting two sealed air chambers.
• Mechanism: Guide vanes deflect bidirectional airflow to drive rotors. Due to symmetrical blade profiles, all rotors rotate in the same direction regardless of airflow direction.
• Variants: Three configurations were tested: Turbine-L1 (1 rotor), Turbine-L2 (2 rotors), and Turbine-L3 (3 rotors).

3. Key Contributions

1. First Integrated Model: Developed the first numerical model capable of fully coupling hydrodynamic (sloshing), aerodynamic (compressible air), and turbo-mechanical (rotor dynamics) behaviors in a wave energy liquid tank.
2. Experimental Validation: Successfully validated the numerical model against scaled prototype tests, demonstrating high accuracy in predicting rotor speed, liquid surface elevation, and air pressure.
3. MLATS Innovation: Introduced and analyzed the Multi-Layered Impulse Air Turbine System, proving its superiority over single-rotor designs in terms of power output and reliability.
4. Parametric Optimization: Systematically identified optimal mechanical parameters (Moment of Inertia, Damping Coefficient, PTO damping) and geometric parameters (Tank Breadth) for maximizing energy harvesting.

4. Key Results

A. Model Accuracy

• The numerical model accurately reproduced experimental data for rotor speed, free-surface elevation, and air pressure across various wave periods ($T = 1.00s - 1.15s$).
• Convergence studies confirmed that a mesh size of ~4.21 million cells and a time step of 0.001s provided sufficient accuracy.

B. Mechanical Parameter Analysis

• Moment of Inertia ($J$): Primarily affects the variation range (stability) of the rotor speed. Higher $J$ results in a more stable rotation with smaller fluctuations, but does not significantly change the average speed.
• Damping Coefficient ($\mu$): Significantly influences the average rotor speed. Lower damping leads to higher average speeds.
• PTO Damping: An optimal PTO damping exists (found around $6\mu_0$ for the tested conditions) that balances torque generation and rotor speed to maximize power output.

C. Efficiency Improvements (MLATS vs. Single Rotor)

• Power Output: Under small-period excitation conditions ($T=0.80s$), upgrading from Turbine-L1 to Turbine-L2 increased average power by ~25%, and to Turbine-L3 by ~40%.
• Non-linear Scaling: Increasing the tank breadth ($B$) boosts power non-linearly. Doubling the tank breadth ($2B_0$) resulted in a four-fold increase in maximum average power output.
• Energy Dissipation: Multi-layered turbines dissipate more liquid motion energy, leading to reduced free-surface amplitudes compared to single-rotor systems, indicating more effective energy extraction.

D. Reliability and Robustness

• Failure Analysis: Simulations of Turbine-L3 with damaged rotors showed remarkable resilience.
  • If the middle rotor (Rotor-2) fails, power loss is only 22%.
  • If a side rotor (Rotor-1 or 3) fails, power loss is 44%.
  • Even in the worst-case scenario (only the middle rotor working), the system retains 14% of its rated capacity.
• Comparison: Unlike conventional single-rotor systems where a turbine failure leads to total system failure, the MLATS design ensures continued operation and power generation even with significant component damage.

5. Significance

This research provides a critical step forward in the commercialization of wave energy:

• Enhanced Survivability: By enclosing the PTO system within a liquid-filled hull and using a robust MLATS design, the device is protected from direct marine exposure, addressing the primary cause of WEC failures.
• Improved Efficiency: The MLATS design and optimized tank geometry significantly overcome the low efficiency barriers of previous pneumatic liquid-tank concepts.
• Reliability: The inherent redundancy of the multi-layered system offers a solution to the "single point of failure" problem common in marine energy devices, making the technology more viable for long-term deployment in extreme ocean conditions.
• Design Framework: The validated integrated numerical model serves as a powerful tool for future optimization of enclosed wave energy converters without the need for extensive physical prototyping.