Influence of Turbulence Length Scale and Platform Surge Motion on Wake Dynamics in Tandem Floating Wind Turbines

This study utilizes high-fidelity CFD simulations to demonstrate that increasing the inflow turbulence integral length scale is the primary factor accelerating wake recovery and enhancing downstream power output in tandem floating wind turbines, as larger scales introduce energetic low-frequency eddies that destabilize tip vortices and promote mixing, while platform surge motion plays a secondary role.

The Gist

The Big Picture: The "Tandem Wind Farm" Problem

Imagine two wind turbines floating on the ocean, one right behind the other. The first turbine (the "Upstream" one) catches the wind and spins, generating electricity. But as it does this, it leaves a messy, slow-moving trail of air behind it, like a boat leaving a wake in the water. This is called the wake.

When the second turbine (the "Downstream" one) tries to catch the wind, it's stuck in this slow, messy trail. It gets less wind, spins slower, and produces much less electricity. In fact, it can lose over 10% of its potential power just because it's standing in the shadow of the first one.

This paper asks a simple question: How can we make that second turbine spin faster?

The researchers looked at two main things that might help:

1. The "Texture" of the Wind: Is the wind smooth and steady, or is it choppy with big, rolling waves of air?
2. The "Dance" of the Platform: Since these turbines are floating, they bob and sway with the waves. Does this movement help or hurt?

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Analogy 1: The "Smooth vs. Choppy" Wind (Turbulence Length Scale)

Think of the wind like a river flowing toward the turbines.

• Small Ripples (Small Turbulence Scale): Imagine a river with tiny, fast ripples. When the first turbine cuts through this, it creates a very organized, tight spiral of slow air behind it. It's like a neat, tight rope of smoke. This "rope" stays together for a long time, blocking the second turbine effectively.
• Big Rolling Waves (Large Turbulence Scale): Now, imagine the river has huge, slow-moving swells. When the first turbine cuts through these big waves, the "rope of smoke" gets shaken apart immediately. The big waves mix the slow air with the fast air around it much faster.

The Discovery: The researchers found that bigger waves in the wind are actually better for the second turbine.
When the wind has these large, rolling structures (called a large "integral length scale"), they act like giant mixers. They break up the slow, dead air behind the first turbine much faster. By the time the air reaches the second turbine, it has recovered its speed and energy.

• The Result: When the wind had these "big waves," the second turbine produced up to 140% more power compared to when the wind was smooth and steady!

Analogy 2: The "Swaying Dancer" (Platform Surge Motion)

Now, imagine the first turbine isn't just standing still; it's floating on a boat that rocks back and forth (surge motion) with the waves.

• The Stationary Turbine: If the first turbine is locked in place, it creates that neat, tight "rope of smoke" (the wake) that stays organized and blocks the second turbine.
• The Swaying Turbine: If the first turbine rocks back and forth, it's like shaking that rope of smoke. The movement distorts the wake, making it wobble and break apart sooner.

The Discovery: A little bit of rocking helps!
When the first turbine sways, it "stirs the pot" of the air behind it. This mixing happens faster, so the second turbine gets better wind.

• However: The researchers found that how the two turbines sway relative to each other (whether they rock in sync or opposite to each other) doesn't matter much. The most important thing is that the first turbine is moving. The second turbine's movement is less critical.

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The "Secret Sauce": Mixing is Key

The whole story comes down to mixing.

Think of the wake as a cup of cold coffee (slow air) sitting in a cup of hot tea (fast wind).

• Without help: The cold coffee sits at the bottom, and the hot tea stays on top. They don't mix well. The second turbine drinks the cold coffee.
• With Big Wind Waves: The big waves act like a giant spoon, stirring the coffee and tea together quickly. The second turbine gets a warm, mixed drink.
• With Swaying: The swaying motion acts like a smaller spoon, also helping to mix things up, but the big waves do the heavy lifting.

Why This Matters for the Future

This study is a game-changer for designing floating wind farms.

1. Stop fighting the waves: Instead of trying to build platforms that stay perfectly still (which is hard and expensive), engineers might realize that allowing the turbines to move with the waves actually helps the farm produce more power.
2. Smart Spacing: We now know that the "texture" of the wind matters more than just how "strong" the wind is. If we know the wind has big, rolling structures, we might be able to place turbines closer together because the wake recovers faster.
3. The "Upstream" Boss: The most important factor is what the first turbine does. If the first turbine is moving or if the wind is "choppy" in a specific way, the second turbine will be happy. The second turbine's own movement matters very little.

The Bottom Line

The paper concludes that chaos is good for wind farms.
Specifically, big, rolling waves of wind and the natural swaying of floating turbines help break up the "dead air" behind the first turbine. This allows the second turbine to catch fresh, fast wind much sooner, turning more electricity and making offshore wind farms more efficient and profitable.

Technical Summary

1. Problem Statement

Floating Offshore Wind Turbines (FOWTs) are critical for future renewable energy, but their performance in arrays is significantly limited by wake interactions. When turbines are arranged in tandem, the downstream turbine operates in the low-momentum, high-turbulence wake of the upstream unit, leading to power losses (often >10%) and increased fatigue loads.

While the influence of turbulence intensity (TI) on wake recovery is well-documented, the specific role of the integral length scale of inflow turbulence (the size of dominant eddies) remains poorly understood, particularly in the context of floating platforms that undergo unsteady motions (surge, pitch, sway). Existing literature often assumes wake recovery is a function of TI alone, neglecting the spectral characteristics of the inflow and the complex coupling between atmospheric turbulence scales and platform dynamics. This study aims to decouple these effects to understand how inflow turbulence structure and platform surge motion jointly govern wake development and power extraction in a tandem FOWT configuration.

2. Methodology

The study employs High-Fidelity Computational Fluid Dynamics (CFD) using Large-Eddy Simulation (LES) to resolve the unsteady flow physics.

• Numerical Framework:

  • Solver: OpenFOAM (v2312) using the pimpleFoam solver for transient, incompressible flow.
  • Turbulence Model: Wall-Adapting Local Eddy-Viscosity (WALE) subgrid-scale (SGS) model for robust near-wall and transitional flow resolution.
  • Turbine Modeling: A Surge-Aware Actuator Line Method (ALM). Unlike standard ALM, this implementation explicitly accounts for the platform's surge velocity ($U_s$) when calculating the relative inflow velocity and angle of attack on blade elements.
  • Inflow Generation: The Divergence-Free Synthetic Eddy Method (DFSEM) generates realistic turbulent inflows. Five distinct integral length scales ($L_u$) were prescribed, ranging from $0.25R$ to $1.25R$ (where $R$ is the rotor radius). Crucially, the study maintained a consistent mean velocity ($U_\infty = 11.4$ m/s) while varying $L_u$, which naturally resulted in varying turbulence intensities (from ~1.9% to 7.2%) due to the physical coupling between scale and intensity.

• Simulation Setup:

  • Configuration: Two NREL 5MW reference turbines in a tandem arrangement, separated by 5 rotor diameters (5D).
  • Motion Scenarios:
    1. Fixed-Fixed (FF): Both turbines stationary.
    2. Surge-Fixed (SF): Upstream turbine surges sinusoidally (Amplitude = 4m, Frequency = 0.63 rad/s); downstream fixed.
    3. Surge-Surge (SS): Both turbines surge, with variations in relative phase ($\Delta\phi = 0$ for in-phase, $\Delta\phi = \pi$ for anti-phase).
  • Grid: Approximately 94 million cells with high refinement near the rotors ($\Delta x \approx 0.0063D$).
  • Validation: The mesh resolution was validated by ensuring the ratio of resolved to total Turbulent Kinetic Energy (TKE) exceeded 0.97 in the wake, satisfying high-quality LES criteria.

3. Key Contributions

• Decoupling Scale and Intensity: The study isolates the effect of the integral length scale ($L_u$) on wake dynamics, demonstrating that larger scales (even with associated higher TI) are the primary drivers of wake breakdown, distinct from intensity alone.
• Surge-Aware ALM: Implementation of a specialized ALM that dynamically updates the apparent inflow velocity based on platform surge motion, capturing the aerodynamic coupling between platform kinematics and rotor loading.
• Mechanism Elucidation: Provides a physics-based explanation of how low-frequency, large-scale eddies interact with tip vortices to trigger earlier wake meandering and mixing, contrasting with classical models that rely solely on turbulence intensity.
• Phase Independence: Demonstrates that while platform motion enhances recovery, the relative phase of surge motion between tandem turbines has a negligible effect on time-averaged power, shifting the focus to upstream wake dynamics rather than downstream motion synchronization.

4. Key Results

A. Influence of Inflow Turbulence Length Scale ($L_u$)

• Wake Recovery: Increasing $L_u$ (from $0.25R$ to $1.25R$) significantly accelerates wake recovery. Larger scales introduce energetic, low-frequency eddies that destabilize the coherent tip-vortex system earlier.
• Velocity Deficit: For the largest scale ($L_u/R = 1.25$), the velocity deficit at the downstream turbine location ($x/D=5$) was reduced by approximately 24% (Fixed-Fixed) and 22% (Surge-Fixed) compared to uniform inflow.
• Power Gains: The downstream turbine power coefficient ($C_P$) increased monotonically with $L_u$.
  • In the Fixed-Fixed case, power gains ranged from +88.5% to +142.3% relative to uniform inflow.
  • In the Surge-Fixed case, gains were more moderate (+5% to +47%) because the surge motion had already induced significant mixing, leaving less room for improvement from turbulence scales alone.
• Mechanism: Large $L_u$ promotes lateral and vertical entrainment, causing the shear layer to thicken and break down faster. This shifts the wake from a coherent, vortex-dominated state to a rapidly mixing turbulent state.

B. Influence of Platform Surge Motion

• Enhanced Mixing: Surge motion of the upstream turbine introduces time-dependent disturbances that thicken the shear layer and promote large-scale unsteadiness. This leads to earlier tip-vortex breakdown and reduced velocity deficits compared to fixed turbines.
• Secondary Role of Phase: When both turbines surge, the relative phase ($\Delta\phi$) between them (in-phase vs. anti-phase) had minimal impact on the mean wake structure and time-averaged power. The wake dynamics were governed primarily by the upstream turbine's motion and the inflow turbulence structure, not the synchronization of the downstream unit.
• Spectral Characteristics: Surge motion broadened the energy spectrum of the wake, shifting energy toward longer wavelengths (lower frequencies), which correlates with enhanced meandering.

C. Interaction of Scale and Motion

• The study found that inflow turbulence scale is the dominant parameter. When strong background turbulence (large $L_u$) is present, the additional benefit of surge motion becomes secondary.
• Conversely, under low-turbulence conditions, surge motion provides a significant boost to wake recovery.

5. Significance and Implications

• Design Optimization: The findings suggest that wind farm layout and control strategies should prioritize the spectral characteristics of the inflow (turbulence scales) rather than just turbulence intensity.
• Control Strategies: Since the relative phase of platform motion has little effect on mean power, complex control strategies aimed at synchronizing platform motions may offer diminishing returns compared to strategies that exploit natural large-scale turbulence or active wake steering.
• Physics-Based Modeling: The study provides a rigorous validation of the coupling between turbulence scales and platform dynamics, offering a more accurate basis for predicting performance in realistic offshore environments where both factors coexist.
• Energy Capture: The results indicate that under realistic offshore conditions (large integral scales), downstream turbines can recover a substantial portion of lost power, potentially increasing the overall capacity factor of floating wind farms by up to 140% relative to uniform inflow assumptions.

In conclusion, this research establishes that upstream wake dynamics, driven by the integral length scale of inflow turbulence and platform surge, are the governing factors for downstream performance in floating wind farms, while the specific phase relationship between turbine motions is a secondary factor.